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Obama to students: You will need algebra
Through education, you can also better yourselves in other ways. You learn how to learn – how to think critically and find solutions to unexpected challenges. I remember we used to ask our teachers, "When am I going to need algebra?" Well, you may not have to solve for x to get a good job or be a good parent. That's true. But you will need to think through tough problems. You will need to think on your feet. So, math teachers, you can tell your students that the President says they need algebra.
I really don't get how solving for x in 3x + 17 = 5x + 2 will "help students think through tough problems [in life]" and "think on their feet." I see algebra skills as useful, but not out of context of the types of problems they help us solve. Instead of students learning an algorithm for which almost none of our students will ever get to see a real application; what if we taught students areas of mathematics which had direct application in their lives, and which actually helped them think?
I think that we do need some people who learn algebra in a really deep way, but the type of algebra that people use in their day to day lives is fairly simple, and doesn't take very long to teach, especially if students see the value in what they are learning. Too long people have learned math because someone said they should.
Well Mr. President, I don't think that telling my students that just because you think it is useful will mean they will want to learn it. I'm going to keep focusing on presenting the mathematics I teach in the context of the lives of my students instead, thank you.
Comments
Although Obama's statement begs a lot of question, I don't think, however, that he meant that you actually need algebra to solve problems in life, but I think what he meant was that the level of focus needed to solve tough problems is present in algebra.
It's amazing the type of critical thinking skills you gain if you keep an open mind about math, and that you dedicate just a little bit of your time to at least solve just one challenging problem, such as 3x + 17 = 5x + 2.
I'll give an example that is sort of off topic: at SFU (and maybe in other Universities as well), it's mandatory for software engineering students to take an introductory course to circuit design. Will software engineers ever need to build circuit boards themselves? No, of course not. That's not what they do. Software engineers work through a series of abstraction, and there absolutely no point in trying to dabble with hardware. Even the professor that taught the circuit design course said that you will never need to know all the nitty gritty details of circuit design. But it sure helps to think critically about how data and instructions are passed from the memory system to the CPU. That way, someone trying to come up with an efficient algorithm to solve a problem will be two steps ahead. Not only will the engineer come up with a solution that is algorithmically efficient (that is, having a very low big-order O), but one that is also physically efficient when it comes to CPU usage.
I'm not saying that you should coerce kids to learn algebra. I'm just saying that the level of thinking required to solve an algebraic problem to find x is at the same level of thinking in the real world. Sure by the time that kids grow up, they will forget a lot of the math stuff, but the one thing that they will retain forever is the ability to stay focused to solve problems, and I think that's what counts, and I think that's what Obama meant.
It probably is what he meant, but my question is, can we find something more engaging for kids to work on and end up with the same result, an adult who is willing to struggle through a problem in order to find a solution?
Kids solve problems every day playing videogames, with a laser-like focus. They strategize, plot courses, engage in basic physics. Not much of that skill transfers to real life though. It takes a huge mental jump and a lot of initiative to bridge one domain to another, and most students won't do it on their own.
The same is more or less true with algebra.
Teaching algebra to teach basic problem solving skill works on some level, but it's about as efficient as trying air condition your back yard. Almost none of the effort that students spend learning algebra will go to anything else in life, even indirectly. And because it goes unused, even direct domain specific knowledge will fade away within a couple years.
Meanwhile, Alan Simpson, who the president appointed to reform Social Security, said recently that it was nonsense to say a phrase like "The average life expectancy of someone that reaches 65 is 78." He literally did not understand why the average life expectancy at 65 would be different than at 12, or at birth.
I bet Alan could solve for x just fine. But, as the cognitive science literature will tell you, skills aren't easily transferable/generalizable, and we never bothered to teach him stats, and because of that a lot of old people may go very cold and hungry. So it really does matter, and matter quite a bit what we choose to teach people -- it really is a matter of life and death, and is that quite frequently.
I agree completely. I didn't think of transfer being a problem, but I can definitely see that it is. Students are expected to learn problem solving skills from algebra and then transfer those skills to the ability to fix a flat in their car, or whatever other problems life throws their way. Not going to happen.
Hey David-- another great post. I'd like to see you flesh out your ideas starting from scratch. If you could design a year-long curriculum that accomplished what Algebra advocates claim Algebra accomplishes, but has that missing ingredient of tangible application I'd be interested for sure.
Mike makes a huge point about domain knowledge. Anyone who has ever worked with smart but "non tech savvy" people know how vital specific knowledge is to problem solving. I can't debug Java because I have no domain knowledge. I can't correct spelling on a French test for the same reason. Deep knowledge is almost the whole game when it comes to problem solving. Without broadening the schema of our students, they will be cut-off from the ability to learn deeply and solve problems in most areas. Some educators claim to want to teach problem solving skills at the expense of a broad schema. Never understood why those beliefs still circulate. Maybe it's because they never read a comment like yours! Valuable piece of the puzzle for sure.
Your analogies are good, and I think they point to an important issue in mathematics education. Many math teachers teach nothing but domain knowledge, and produce kids that can't solve real problems. So domain knowledge isn't everything. Similarly, as you point out, student's can't solve any problems if they don't have the tools. So we need to teach both domain knowledge and the problem solving tools students need to be able to move on in their lives. Since we are teaching hardly any of the problem solving skills in mathematics, and ending up with a largely innumerate public, I think we should teach more of the problem solving and less of the domain knowledge.
I'm not sure exactly what that looks like yet. I'm still thinking about it, and think I am not qualified to make that determination alone. I am working with a small team right now of other progressive mathematics educators interested in improving mathematics instruction in the same way.
re: "Many math teachers teach nothing but domain knowledge, and produce kids that can't solve real problems." I think that is essentially what Mike was talking about. There is no real thing as "problem solving skills" there is just a certain amount of domain knowledge needed to solve a specific problem.
Understanding how my lawn mower works is all I really need to be able to know how to solve any problem with it. Knowing how my lawn mower works doesn't help me figure out why my soccer team can't breakdown a defense at midfield. In order to solve my soccer problem, I need to know a lot about soccer. Knowing Algebra doesn't really help me fix that lawn mower either. Understanding Algebra might help me understand more about the relationships between numbers though, which might help me in other areas of math. Understanding how my lawn mower works might help me fix a go-cart or a motorcycle because there are similar patterns and vocabulary and materials involved, meaning, I already have *some* of that domain knowledge or I can more easily add new info to my schema because I have a solid foundation in "motors" or "combustion" or whatever.
"Problem solving skills" is a phrase that doesn't have much real meaning. Asking people to use strategies like "take a break and look at it fresh tomorrow" or "examine your assumptions and see if your assuming something to be true that isn't true" are certainly helpful reminders, but they are a miniscule part of problem solving. "Problem solving ability" essentially = "level of domain knowledge."
I might add that confidence/freedom to act is an important part of the equation, but that *usually* comes with experience as well. Sometimes students are capable of solving a problem, they have the know-how, but they are afraid for some reason. In those cases, domain knowledge is insufficient. I am not saying domain knowledge is everything, but it is an overwhelmingly large piece of the puzzle.
To put it in numbers, maybe 95% of problem solving is simply domain knowledge coupled with freedom to act on that knowledge.
Boy, I can't say I agree with that. The problem with domain level knowledge is that it comes from someone else, and is tied to their understanding of the situation, not yours. The more domain knowledge you learn, the less able you are to think about that domain knowledge outside of the language constructed around it. In other words, being deeply entrenched in domain knowledge is to be entrenched in the ideas of others, which limits your ability to think creatively about the problem.
If we carefully instructed all of our students in the ideologies of environmentalism, for example, whatever lense we chose to share those ideologies would become the lens through which they would examine all new instances of environmental problems. Ask a typical politician about the environment for example, and because they've been so deeply rooted in the economic model of environmentalism, they can't see solutions to problems outside of that domain.
I think your example proves the opposite point though-- asking a politician how to solve problems with our global ecosystem is a bad idea because they have virtually zero domain knowledge. I think climate scientists have a much better chance of finding root causes to environmental problems because they understand the subject better. Plus, hey have a much more developed schema to weave new knowledge into.
The solution they come up with might be something like "we need some way to build taller buildings, or invent new drainage systems or something. They would be poor choices to pick to actually build those things though because they have no domain knowledge. Engineers, on the other hand, have that domain knowledge so they would be better to solve those problems. People can't solve any problem without specific domain knowledge of the problem area. You don't necessarily need to be a master to begin solving problems, but the more knowledge you have the better chance you have to solve the problem. Not only that, but the more knowledge you have, the better chance you have to learn more about the problem on your own in the future.
If someone actually was 95% steeped in the domain knowledge of others, how would they look at the problem from a fresh perspective? Further, achieving such a high level of domain knowledge in students is only possible through a standardization of the curriculum. Do we really want all kids to have the same understanding of the issues relevant to our world? How could we possibly find solutions?
Some of the freshest and best approaches to solving problems have come from amateurs and people outside of the field. Cross-pollination of fields has produced some of the most amazing ideas. The entire field of chaos theory, essentially invented by Lorenz, happened because a mathematician (and a nonstandard one at that) explored an area outside of his original expertise, meteorology.
Not sure what you mean by "95% steeped in the domain knowledge of others."
Are you saying that 7x7=49 to you because you are being influenced by people who knew this before you were born? If someone with no knowledge of multiplication looked at 7x7, they might find a different, better answer?
Totally confused.
How about this-- can you give me at least one example of a problem in math that people can solve without domain knowledge? If I couldn't add, subtract multiply or divide and I didn't know what the number values were or what any formulas were or anything in the domain, what problem could I solve with problem solving skills alone?
Also- can you give an example of a "problem solving skill?" What would you teach someone instead of building their schema? You are advocating sacrificing domain knowledge and increasing problem solving skills, but I don't understand what you mean by that. Can you give me a concrete example?
Now you are being ridiculous, and not reading my post correctly. When did I say that domain knowledge was completely pointless? Obviously I can't solve any problems without some domain knowledge, but to think that you need absolutely every piece of the puzzle in order to solve problems is also completely crazy in my mind. When in life do we actually have every piece of the puzzle?
As for your second question, there are a few things kids need to be able to do to solve problems.
For simple problems, they need to know how to find the answer when they don't know it.
For more complex problems, they need to know how to build a team of people capable of working on the problem.
Students need to be able to communicate what they know in a variety of representations. This means to me, being able to write about the problem, graph it, map it out, create multimedia representations for sharing with an audience, and a whole lot of other representations.
They need to look at "the problem" from different perspectives. What are the cultural implications of this problem? What are the environmental consequences of this solution?
They need to be able to look at a problem and even recognize what they know, what their social circle knows, and what other people know about the problem. This is also called researching the problem.
They need to be able to deconstruct problems into smaller "chewable" pieces. Take a big problem, find the smaller sub-problems, and then distribute those among their community to solve. If there are only a few pieces of problem to chew on, then obviously they can solve it themselves.
David, not being ridiculous. Trying to understand the comment about "domain knowledge of others". You seemed to imply that domain knowledge was something that hurts problem solving. I am guessing what you meant to imply is that people can teach other people misleading things and give them a false sense of having acquired knowledge. I agree that if someone has the wrong answers to questions, those answers will not help them solve problems. We agree on that, if that was what you meant.
If you were saying all knowledge we learn from books, teachers, TV, radio, friends, is somehow wrong . . . I don't know how to respond to that.
re: "to think that you need absolutely every piece of the puzzle in order to solve problems is also completely crazy in my mind." I agree. I don't even think it is possible to know everything there is to know about a subject. The inescapable fact though is that the more we know about something, the better chance we have to solve problems that arise in that domain. If we know a little, we can solve some problems. If we know a lot we can solve many problems. I don't think anyone would debate that. There is a direct relationship between domain knowledge and problem solving ability.
The Lorenz example is a perfect illustration of how important domain knowledge is to problem solving. Lorenz was a mathematician. If he was a janitor or a sportcaster or a basket weaver, the fact that he solved a math/weather problem would be unusual. The fact that he took his domain knowledge of math and then added to it an extensive set of really knowledge from the domain of meteorology, underscores the fact that he was possibly the *most likely* person on earth to uncover chaos theory. He was able to see what others couldn't because he had more knowledge of the domains than others did. Mathematicians don't know weather and meteorologists don't know math well enough. He knew both. His domain knowledge separated him from others.
His story is a great example of why building not just a deep schema, but a *broad* schema is so valuable. When we know a lot about a few different subjects, we can make connections and see things others who lack our knowledge can't see.
I think everything on your list is just another way to emphasize the value of domain knowledge. I think we are actually saying the same thing just using different words.
re: finding answers/building teams-- I am saying we can't solve problems without domain knowledge. You are saying we can, just find people that have that knowledge or find a resource where you can learn it. Same difference to me. Either way, the problem doesn't get solved without domain knowledge. It is the only piece of the problem solving puzzle that is mandatory. I think we both agree on that, no?
re: variety of representations-- not sure what sharing via multimedia has to do with solving a problem. If the specific problem they are solving is "how do I communicate X to others?" then having knowledge of multimedia tools will help them find a solution, but for most problems, multi-media presentation tools are not applicable. Fixing that lawnmower takes knowledge of lawnmowers, not multi-media presentation tools.
My understanding is that the goal is not to teach kids how to get other people to solve their problems, but to help build within them the ability to solve their own problems. teaching kids how to ask for help when they can't solve a problem on their own is great. I lean on people all the time. It doesn't help me learn to be a better problem solver though- it helps the person who solves my problem for me. What helps me become better is learning why the solution they proposed worked/didn't work. That knowledge adds to my understanding in that domain and may help me solve my own problem in the future.
re: Cultural implications and consequences-- these skills assume that the problem solver has or will need to have domain knowledge to come up with answers. Can't know the repercussions of something you don't understand. If I don't understand gravity, the repercussions of space travel on my bones will be a terrible shock to me. If I know about gravity and bones, I will have a better understanding of the consequences.
re: research- Researching is defined as a way to increase your domain knowledge when you don't have enough to solve the problem. I agree this is vital. The more knowledge we have, the more problems we can solve.
I agree with all of this information, excepting that multimedia representations is pretty broad and would include pictures and diagrams, so a lawnmower-fixing-person might absolutely have to be able to explain their problem using a picture, or a diagram to explain exactly where the problem is if they are unable to solve the problem themselves.
Where I think we differ is when this gathering of domain knowledge occurs. Should it occur during school, in an out of context setting, or should it occur when the person actually needs the knowledge? I'd prefer to see people who knew a lot about finding accurate, reliable, and useful information about an area of need, and perhaps a bit less than we do now of people expecting to know everything about a topic when they leave school. In other words, in our current system, I think we spend way too much time front-loading kids with information, in the expectation that they will find it useful, and not nearly enough time spending time actually finding useful information for themselves.
A consequence of this, is that sites like Answers.com and similar junky-user-entered-info-with-lots-of-ads profilerate through the web, and people have very little idea on how to actually find useful information. I was talking about this problem with our school librarian, and she was complaining that kids just do random Google searches to find information, and lack any kind of critical awareness of the reliability of that information. She said that the student at the very least should check to see if the article they are reading has references. So I opened up a textbook, and pointed out that traditional textbooks lack references as well.
I know what your counterargument will be, which is that people who have vast exposure to domain level knowledge can spot the BS more easily than people with little exposure to domain knowledge. However, it's always a trade-off. We can't possible train the kids in everything they could be exposed to, so we might be better off giving them a moderate amount of domain knowledge in a broader range of topics, and focusing on techniques they can use to establish the reliability of new knowledge.
However, there is also value when people make leaps and try to fill in gaps in their existing domain knowledge. Most of the time, they get it wrong, but once in a while they stumble across a different perspective in the gap, and it ends up re-arranging our existing knowledge in an area. It feels to me like your perspective on domain knowledge is that of a static representation of the world, when in fact I see our knowledge over time as having been dynamic. We know the world differently than we used to, our perspective on it has changed. How has that happened? At least occasionally, there are people muddling around and messing around and making assumptions about the world, and at least some of these assumptions change the nature of what we know. While domain knowledge is absolutely important for expanding areas of knowledge, too much of it is a hindrance in terms of finding flaws with existing knowledge.
I agree, it is a trade-off. The tug of war between depth and breadth is tricky.
The deeper the knowledge, the more higher-order thinking skills begin to emerge. Critical thinking, problem solving, etc., all emerge only after a certain tipping point. "Covering" a lot of different material (in a surface way) prevents these higher-order thinking skills from emerging. I think this is the real issue with increasing the importance of fact-based testing in many schools-- standardized test designers value breadth over depth.
The broader the knowledge, the greater the student's ability to learn new things in the future. We can only learn things that connect to our current schema, so leaving things out of the curriculum basically eliminates a student's ability to learn those things later in life. It's not impossible, but it makes it highly unlikely that a student will learn that thing from scratch later in life. This is the reason why millions of Mexican children speak Spanish, but millions of American (or Canadian) adults who want to learn Spanish never do.
In some ways it is a balancing act between higher-order thinking ability and the ability to be a life-long learner. Keeping both of those plates spinning is the difficult part.
Yes, we completely agree on this. Finding the right balance point is the tricky part. Right now, I think we are too far on the content area of the spectrum, but as you point out, we have to be careful not to go too far in the other direction.
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Overview - MATHEMATICS FOR THE NEW SPEAKERS OF ENGLISH - TEACHER
The 161-page Student Text provides lessons and activities that develop mathematical understanding as well as English usage and vocabulary skills. Teacher's Guide has notes, answer key, and chapter-by-chapter instruction.
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use of technology in the Dugopolski precalculus series for 1999 is optional. Thus, instructors may who plan to study additional mathematics, this text provides the skills, understanding and ... MOREinsights necessary for success in future courses. For students who do not plan to pursue mathematics further, the emphasis on applications and modeling demonstrates the usefulness and applicability of mathematics in today's world. Additionally, the author's focus on problem solving provides numerous opportunities for students to reason and think their way through problems. The mathematics presented here is interesting, useful, and worth studying. One of the author's principal goals in writing this text is to get students to feel the same way. Providing Strategies for Success: This including highlights, exercise hints, art annotations, critical thinking exercises, and pop quizzes, as well as procedures, strategies, and summaries.
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Syllabus: MAT 411-01 Mathematical Modeling. Spring 2013
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In this course we will practice using math as a tool to
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Text
A Course in Mathematical Modeling by Douglas Mooney
and Randall Smith. Mathematical Association of America, 1999.
Learning Outcomes
Computer skills
We will use free computer software as a labor-saving tool for
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Unit specification
Aims
The programme unit aims to introduce the basic concepts of limit and convergence
(of real sequences, series and functions) and to indicate how these are treated
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Brief description
The first part of the course discusses the convergence of real sequences
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On completion of this unit successful students will be able to:
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Future topics requiring this course unit
Real analysis is needed in more advanced courses in analysis, functional
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MATH20142 Complex Analysis extends the ideas in this course to functions of
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9780321849250 Approach to Mathematics for Elementary School Teachers since its first edition, and it remains the gold standard today. This text not only helps students learn the material by promoting active learning and developing skills and concepts—it also provides an invaluable reference to future teachers by including professional development features and discussions of today's standards. The Eleventh Edition is streamlined to keep students focused on what is most important. The Common Core State Standards (CCSS) have been integrated into the book to keep current with educational developments. The Annotated Instructor's Edition offers new Integrating Mathematics and Pedagogy (IMAP) video annotations, in addition to activity manual and e-manipulative CD annotations, to make it easier to incorporate active learning into your course. MyMathLab® is available to offer auto-graded exercises, course management, and classroom resources for future teachers. To see available supplements that will enliven your course with activities, classroom videos, and professional development for future teachers, visit «Show less... Show more»
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"Worldwide AP Calculus" takes, what has become, a non-standard approach in the topics covered and their ordering. The textbook does not try to "teach to the test." An Advanced Placement course is designed to provide students with the necessary background and skills for advanced placement into their respective college curricula. Too often, modern AP Calculus textbooks have one goal: to optimize students' grades on the AP Calculus exam, regardless of how well the students may end up being prepared to be placed at advanced points in college curricula.
Thus, the content in "Worldwide AP Calculus" is the same material that students would see when using a Calculus textbook in a college or university; so that, while they will be prepared for the AP exam at the end of the course, they will also have the knowledge they need to move on to higher-level math courses when they enter college. The book is a combination of Massey's Worldwide Differential Calculus and Worldwide Integral Calculus for easier use in the AP Calculus classroom setting. This textbook can be used in both an AB and a BC course, and also allows students who are continuing on to AP Calculus BC, after completing AB, to need only one textbook for both courses.
The chatty exposition throughout "Worldwide AP Calculus" is meant to make the textbook more readable for students. However, despite the informal style in the discussions, the mathematics in "Worldwide AP Calculus" is completely rigorous. The precise, rigorous statements of definitions, theorems, and proofs are intended to eliminate the confusion caused by the ambiguity and imprecision of many current AP Calculus textbooks. While we do not expect students to be held accountable on tests for so many technicalities, we feel that it is an important aspect of any mathematics course for the students to understand that the mathematically rigorous statements and results actually exist; furthermore, "Worldwide AP Calculus" provides a resource for those students and teachers who are interested in a deeper, more careful, study of Calculus, beyond what will be tested.
Digital resources also set this book apart from the alternatives. At the beginning of each section, there is a full-length lecture video by the author, which provides additional help to students, while also allowing students to keep up with the course if they miss a class. In addition, there are 5-10 selected exercise video-solutions at the end of each section, for students to watch if they have trouble on homework problems. All of these resources are linked to in the .pdf version of the book, but are also available on our YouTube channel for fast and reliable viewing.
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mathematical expressions, equations, graphs, and other topics in a year long alge- bra course. Topics included are real numbers, simplifying real number expressions with and without variables, solving linear equations and inequalities, solving quad- ratic equations, graphing linear and quadratic equations, polynomials, factoring, linear patterns, linear systems of equality and inequality, simple matrices, se- quences, and radicals. Assessments within the course include multiple-choice, shortanswer, or extended response questions. Also included in this course are self- check quizzes, audio tutorials, and interactive games.
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Provider: Aventa
Algebra II
In this course students will use their prior knowledge from previous courses to learn and apply Algebra II skills. This course will include topics such as functions, radical functions, rational functions, exponential and logarithmic
functions,
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'TRIGONOMETRY – THE WAY TO DO IT' (Ages 15 to 17)
Our complete Trigonometry course contains:
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Trigonometry looks at the relationship between angles and sides in triangles. This book teaches trigonometry from foundations, progressing smoothly from right – angled triangles on to non – right – angled triangles.
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Formula Editor
Mathematics uses symbols that most text editors can't produce, so we've created the formula editor. This gives teachers the ability to create mathematics formulas directly in the material they are working on. With the formula editor, teachers can embed example formulas and problems directly in assignments, tests or classroom exercises – and learners can also create formulas when showing their answers.
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Jacumba Precalculus have worked with university and industry scientists analyzing data from simple and complex experiments on people and animals. I have published papers. I have written grant proposals and IRB submissionsImprove your chances at succeeding in school and being hired for a job by improving your grammar. Excel is a very useful program for a variety of reasons. A few examples are making graphs, performing multiple math computations at once, and manipulating data.
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Baruch College's Student Academic Consulting Center links to sample handouts and exams for some of Baruch's math classes, as well as math tutorial videos in Baruch's Digital Media Library. Video tutorials include college algebra, precalculus, and calculus. You must have a web browser with a plugin capable of playing QuickTime movies to view these videos.
Calculus+ is a series of tutorials in precalculus, calculus, linear algebra, and differential equations, using Maple 8 or higher. These projects were developed by CUNY faculty and tested in CUNY classrooms from 1998-2004.
Wolfram|Alpha, the Wolfram "computational knowledge engine", calculates answers to various questions using Mathematica packages and data from multiple online sources.
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The Tricki, a "a repository of mathematical know-how," is a wiki which seeks to codify methods of mathematical technique and problem-solving
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Pythagoras, ancient Greek mathematician and religious leader, believed that all existence could be described with whole numbers.
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Learn the math that will propel you to great heights. A class to help hone the skills that you will need to build toward higher math and understanding the world around you. Limits, derivatives, integrals: the building blocks of technology today and the world around us.
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concept of understanding in mathematics with regard to mathematics education is considered in this volume. The main problem for mathematics teachers being how to facilitate their students' understanding of the mathematics being taught. In combining elements of maths, philosophy, logic, linguistics and the psychology of maths education from her own and European research, Dr Sierpinska considers the contributions of the social and cultural contexts to understanding. The outcome is an insight into both mathematics and understanding.
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The mathematics curriculum presents a vision of mathematics that is designed to meet the diverse needs of students in every school and student. The curriculum represents high academic standards across a broad spectrum of mathematics topics. It establishes the basis for a challenging program of study that will increase student achievement in mathematics.
The mathematical topics are organized by strands: Algebra, Data Analysis, and Probability, Measurement, Number and Operations, Geometry. These strands extend the K-12 mathematics, providing continuity, and ensuring a smooth transition across elementary, middle, and high school programs. Algebra is listed as a topic in the K-5 curriculum to alert K-5 teachers that the foundation of algebraic skills is being formed at the elementary level.
The mathematics curriculum is designed to support teachers as they instructionally maximize each child's mathematical experiences. Teachers are urged to provide for movement through the curriculum regardless of a student's current grade level. The use of concrete objects (manipulatives) and visual models is vital for students to understand concepts and explore processes. Knowledge acquisition requires a transition from concrete through pictorial, to the more abstract for all students at all levels and ages.
Incorporating technology in instruction is imperative in order to empower students to keep pace with the information age and to be competitive in the job market; it will enhance and provide flexibility in the learning environment. Calculators and computers are essential tools for learning and doing mathematics at all grade levels. Students should be able to solve practical problems, investigate patterns, explore strategies, and focus on the process of solving problems rather than on tedious computation unrelated to applications.
Communication is a vital link. Thinking, speaking, writing, and applying mathematics are invaluable assets. Teaching students these skills can be facilitated through questioning, discussions, reports, projects, journals, oral presentations, experiments, summarizing collected data, and hypothesizing. Collectively, these experiences help students make transitions between informal, intuitive ideas to more abstract and symbolic mathematics language. Reading, writing, and discussing mathematics promote clarity of thought and facilitate deeper understanding of concepts and ideas. Students will improve and gain confidence in their own abilities to explain.
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PEX Quantitative Literacy
GenEd Quantitative Literacy courses present mathematical thinking as a tool for solving everyday problems, and as a way of understanding how to represent aspects of a complexworld. They are designed to prepare students as citizens and voters to have the ability to think critically about quantitative statements, to recognize when they are misleading or false, and to appreciate how they relate to significant social or political issues. While computation may be part a QL course, the primary focus is not computational skills.
Quantitative Literacy courses are intended to teach students how to:
Understand quantitative models that describe real world phenomena and recognize limitations of those models;
Perform simple mathematical computations associated with a quantitative model and make conclusions based on the results;
Recognize, use, and appreciate mathematical thinking for solving problems that are part of everyday life;
Understand the various sources of uncertainty and error in empirical data;
Retrieve, organize, and analyze data associated with a quantitative model; and
Communicate logical arguments and their conclusions.
Courses
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McGahee Mathematics Offers a New Math Tutoring Website
San Diego, CA – McGahee Mathematics is a new math tutoring website that opened in January of 2013. McGahee Mathematics services include math tutoring using various formats. McGahee Mathematics helps in algebra, trigonometry and calculus.
Ben McGahee, owner of McGahee Mathematics is the math tutor and he assists with mathematics tutoring online, in videos and with worksheets. There are several math books out there and McGahee is the author of a new math book that focuses on math fundamentals.
McGahee customizes his tutoring through various mediums including video, worksheets and specialized books. He said that his goal is to suit the academic needs of his clients.
McGahee is also the author of specialized curriculums for each of his students. He has a philosophy that focuses on the application of math techniques and theory. He wants his students to learn how to do the math.
McGahee said, "The McGahee Mathematics philosophy is that the best way to learn math is by doing math."
McGahee Mathematics' owner, Ben McGahee is an author of a brand new book called Foundational Mathematics. The book gives the fundamental on foundational mathematical topics including algebra, geometry, trigonometry and calculus. McGahee is also the author of specialized curriculums for each of his students. He has a philosophy that focuses on the application of math techniques and theory. He wants his student to learn how to do the math.
Foundational Mathematics is an ideal reference for students majoring in mathematics, science and engineering. Anyone needing a refresher course on the basics of mathematics is strongly encouraged to review the book.
About McGahee
McGahee Mathematics is a company that serves the educational needs of students of all skill levels. McGahee Mathematics provides both in-person and online math tutoring services at affordable rates.
You can learn more about McGahee Mathematics and Ben McGahee's work online by visiting McGahee Mathematics at their website at by clicking on the above link. You can also learn more about McGahee's techniques at the McGahee Mathematics' Youtube page. Visit the above websites for more information on McGahee Mathematics and its services
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MATHEMATICS
Mathematics is a powerful tool for solving practical problems, as well as a highly creative field of
study, combining logic and precision with intuition and imagination. A major goal of mathematics
is to reveal and explain patterns, whether the patterns appear in the arrangement of swirls on a
pinecone, fluctuations in the value of currency, or as the detail in an abstract geometric figure.
As Reformed Christians, we believe that God has created, redeemed, and still sustains every
aspect of the world around us. It is our task to appreciate the beauty and well-orderedness of
his creation and to use our God-given abilities to subdue it and to use it for his purposes. Thus,
the aim of the mathematics department is to use analytical thinking to help prepare students to
be Christians who are qualified and professional in their chosen vocations. This is accomplished
in three ways: we work to develop students who are proficient in mathematics, to educate
students for a life of Christian service, and to develop in the students good work habits. The
proficiency in mathematics requires the background, skills, and analytical thinking necessary for
these students to succeed professionally in their chosen work environment: graduate school,
industry, or the elementary or secondary school classroom. The secondary mathematics education
major is designed for teachers in grades 6 through 12. This program meets the major graduation
requirements only for students completing the secondary education certification program.
Trinity Christian College's proximity to metropolitan Chicago offers its mathematics majors
unique education and employment advantages. The wide diversity of industry, business, and
institutions near Trinity allow for a broad range of internship opportunities. Trinity's math
department is an active participant in the mathematics division of the Association of Colleges
in the Chicago Area (ACCA) and the Illinois Section of the Mathematical Association of
America (ISMAA). Activities include area-wide competitions, lectures and conferences, and
annual opportunities for presentations of student research. The department sponsors annual
Mathematics Triathlon competitions for students in grades 3 through 8 from area Christian
schools.
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Tips for simplifying tricky operations Get the skills you need to solve problems and equations and be ready for algebra class Whether you're a student preparing to take algebra or a parent who wants to brush up on basic math, this fun, friendly guide has the tools you need to get in gear. From positive, negative, and whole numbers to fractions, decimals,... more...,... more...
Improve your score on the Analytical Reasoning portion of the LSAT If you're like most test-takers, you find the infamous Analytical Reasoning or "Logic Games" section of the LSAT to be the most elusive and troublesome. Now there's help! LSAT Logic Games For Dummies takes the puzzlement out of the Analytical Reasoning section of the exam and shows... more...... more...
Manage your time and ace the mathematics section of the SAT Scoring well on the mathematics section of the SAT exam isn't guaranteed by getting good grades in Algebra and Geometry. Turn to SAT Math For Dummies for expert advice on translating your classroom success into top scores. Loaded with test-taking strategies, two practice tests, and hundreds... more...
Multiply your chances of success on the ACT Math Test The ACT Mathematics Test is a 60-question, 60-minute subtest designed to measure the mathematical skills students have typically acquired in courses taken by the end of 11th grade, and is generally considered to be the most challenging section of the ACT. ACT Math For Dummies is an approachable,... more...... more...
The fun and easy way® to understand the basic concepts and problems of pre-algebra Whether you're a student preparing to take algebra or a parent who needs a handy reference to help kids study, this easy-to-understand guide has the tools you need to get in gear. From exponents, square roots, and absolute value to fractions, decimals, and percents,... more...
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Site Reviews
Alan Selby's Lessons and Appetizers for Math and Logic Three Skills For
Algebra (a first image of mathematics after arithmetic - why letters or
symbols are favored in algebra in place of numbers); Two logic puzzles to
show the difference between a one-way and a two-way rule; Painless
Theorem Proving; Longer Chains of Reason: What is Mathematical
Induction?; Complex numbers Etc. - A geometrical story based on the
addition and multiplication of arrows in the plane; Chains of Reason -
math-free examples of rule-based reasoning; How Logic or Rule-Based
Reason Appears in Math; VNR Concise Encyclopedia of Mathematics.
Several puzzles and short discussions to help students understand algebra
and proofs. If you don't like the first one you look at, try another;
they're all quite different.
1996 - Magellan, the McKinley InternetWhat are the ideas behind most high school math? ... commentary and
online books ... provide a very rich guide to mathematical reasoning and
high school math to calculus. The emphasis here is on the thinking
part of math rather than the actual manipulations . ...Since July 1995, this ... site has been offering ... lessons to aid and
REFORM instruction in mathematics, logic and science. ... Math-free
lessons on Euclidean Logic may lessen gullibility while developing
precision reading and writing. ...
... offers appetizers and lessons for math from arithmetic to calculus or
why slopes; for deductive reason (logic) and critical thinking; and for
learning in general. Included here are opinions on the communication of
skills and mathematics instruction. ... Each appetizer is different. If
one is not to your liking try another. Most are from ... books on
understanding and explaining math and reason.
Complete Record Details
Since we last featured the complex numbers section of Alan Selby's site
"Appetizers and Lessons for Mathematics and Reason" in March this year,
he has added a new section, Mathematics Education Revisited -
mathematics_education_essays.
Selby has also included a section called POMME: Progressive Observable
Motivated Mathematics Education, which he describes as "a two-level
program for practical mathematics instruction."
Note: POMME and site mathematics education essays
are subsections of the site online archive - another site
section.
WHYSLOPES.COM REVAMPED: Alan Selby has overhauled his website of
"appetizers and lessons for mathematics and reason." Look for the math
formulas neatly typeset with LaTeX, Flash videos, and other rich media
supported by his new content management system.
2011 Math Forum, Internet News 16.51 (23 December)
WHYSLOPES.COM UPDATED
Alan Selby recently posted a five phase framework for mathematics skill
development at his site. The essay "Which Way to Go" introduces it in
plain language:
Notes: Replaced links to old locations by links to newer
location. The site frontpage essentially gives a simpler framework
based on three mutually supportive groups of ends and values for
mathematics and logic education.
Alan Selby has added a new section to his site, entitled "Secondary
Mathematics for Ages 11+, a Practical Approach." "Secondary
Mathematics" provides a coherent guide to technical innovations that
simplify the learning and teaching of arithmetic and number theory
practices, elementary and advanced algebra, elementary and advanced
geometry. The new section ends with two calculus previews with a
description of a light calculus course, more descriptive than
deductive, aimed at introducing the key ideas in differential and
integral calculus. The appendix "Calculus with Proofs for the Keen or
Gifted" describes how to reform calculus.
To better reflect his site's extent and intent, Selby has also re-named
his site -- originally called "Appetizers and Lessons for Mathematics
and Reason," and now "Logic and Mathematics Skill and Concept
Development."
Note: Replaced links to old locations by links to
newer location. This practical approach also includes two chapters
with calculus reform ideas that are promising but not yet rigourously
developed. Refinement of site ideas for precalculus instruction and
light calculus preview has more immediate value for mathematics
education. Site refinement and editing of site ideas for easing
calculus mastery using Lipshitz continuity and decimal views of it,
continuity in general and convergence may come later. There is no
guarantee that the fuller development of these ideas will make
greater rigour in calculus easier to understand and explain
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Description of Saxon Math 5/4: Homeschool KitKit includes Student Textbook, Tests/Worksheets Book, and Solutions Manual with step-by-step solutions to every lesson, investigation and test problem, along with answers to supplemental and facts practice problems
Saxon math has great results, if used the way intended. Saxon builds on itself and intruduces concepts slowly and provides LOTS of practice. In order to master the concepts, all pages should be completed, even if it is very tempting to skip.
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For Test Takers
Introduction to the Quantitative Reasoning Measure
The Quantitative Reasoning measure of the GRE® revised General Test assesses your:
basic mathematical skills
understanding of elementary mathematical concepts
ability to reason quantitatively and to model and solve problems with quantitative methods
Some of the questions in the measure are posed in real-life settings, while others are posed in purely mathematical settings. The skills, concepts and abilities are tested in the four content areas below:
Arithmetic topics include properties and types of integers, such as divisibility, factorization, prime numbers, remainders and odd and even integers; arithmetic operations, exponents and roots; and concepts such as estimation, percent, ratio, rate, absolute value, the number line, decimal representation and sequences of numbers.
Algebra topics include operations with exponents; factoring and simplifying algebraic expressions; relations, functions, equations and inequalities; solving linear and quadratic equations and inequalities; solving simultaneous equations and inequalities; setting up equations to solve word problems; and coordinate geometry, including graphs of functions, equations and inequalities, intercepts and slopes of lines.
Geometry topics include parallel and perpendicular lines, circles, triangles — including isosceles, equilateral and 30°-60°-90° triangles — quadrilaterals, other polygons, congruent and similar figures, three-dimensional figures, area, perimeter, volume, the Pythagorean theorem and angle measurement in degrees. The ability to construct proofs is not tested.
Data analysis topics include basic descriptive statistics, such as mean, median, mode, range, standard deviation, interquartile range, quartiles and percentiles; interpretation of data in tables and graphs, such as line graphs, bar graphs, circle graphs, boxplots, scatterplots and frequency distributions; elementary probability, such as probabilities of compound events and independent events; random variables and probability distributions, including normal distributions; and counting methods, such as combinations, permutations and Venn diagrams. These topics are typically taught in high school algebra courses or introductory statistics courses. Inferential statistics is not tested.
The content in these areas includes high school mathematics and statistics at a level that is generally no higher than a second course in algebra; it does not include trigonometry, calculus or other higher-level mathematics. The Math Review provides detailed information about the content of the Quantitative Reasoning measure.
The mathematical symbols, terminology and conventions used in the Quantitative Reasoning measure are those that are standard at the high school level. For example, the positive direction of a number line is to the right, distances are nonnegative and prime numbers are greater than 1. Whenever nonstandard notation is used in a question, it is explicitly introduced in the question.
In addition to conventions, there are some assumptions about numbers and geometric figures that are used in the Quantitative Reasoning measure. Two of these assumptions are (i) all numbers used are real numbers and (ii) geometric figures are not necessarily drawn to scale. More about conventions and assumptions appears in Mathematical Conventions.
Quantitative Reasoning Question Types
The Quantitative Reasoning measure has four types of questions. Click on the links below to get a closer look at each, including sample questions with rationales.
Each question appears either independently as a discrete question or as part of a set of questions called a Data Interpretation set. All of the questions in a Data Interpretation set are based on the same data presented in tables, graphs or other displays of data.
You are allowed to use a basic calculator on the Quantitative Reasoning measure. For the computer-based test, the calculator is provided on-screen. For the paper-based test, a handheld calculator is provided at the test center. Read more about using the calculator.
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Aims: To consolidate and extend topics met at A-level.
To improve students' fluency and understanding of the basic techniques required for engineering analysis.
Learning Outcomes: After taking this unit the student should be able to:
Handle circular and hyperbolic functions, and sketch curves. Differentiate and integrate elementary functions, products of functions etc.
Use complex numbers.
Employ standard vector and matrix techniques for geometrical purposes. Determine the Fourier series of a periodic function.
Understand power series representations of functions and their convergence properties.
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Neptune PrecalculusSolutions to problems and analysis of topics are mastered by applying logic, step by step processing, and introducing strategies that can assist quickly when used repetitively. I believe in developing a deeper understanding of the topic through comparisons and applications, and presenting the leAlso
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You will solve equations, graph, use formulas, etc. If you are somewhat nervous about this course, that is normal. But don't worry, we will get through this together. I will do my part to help you achieve your goals by teaching you, encouraging you, and getting you on the right course. My goal is for all of my students to pass this course but you must also do your part. These are the things you need to do:
1.Come to class everyday (except in case of an emergency, of course).
2.Come prepared. (Bring notebook, pencil, etc.)
3.Write the bell ringers down (mathstarter/warmup) and try to solve the problems. This is especially important for the 9th and 10th graders. The bell ringers help prepare you for the iLeap and GEE test.
4.Take notes and Ask Questions!!! This is where a lot of students mess up. I know it requires work - paying attention, using your hands to write, ... but I have confidence that you can do it. Anything I write on the board, you need to write down. If you don't have notes, what will you use to study or help you do your homework? Do not be afraid to ask questions. I will be more than happy to answer any question you have pertaining to the lesson.
5.Do your homework. Doing your homework lets you know if you understand a concept. It also prepares you for your test.
6.If you need more help, go to the websites on my resource page and come to tutoring.
If you do All of the Above, I truly believe that you can pass this course. It's your choice, so make the right one.
class material
Supply List
The following materials are needed and should be brought to class everyday.
1 to 1 1/2 in binder
pack of dividers
looseleaf paper
pencils
red pen or color pen, excluding black or blue
two(2) dry erase marker(preferably expo black)
calculator ( Scientific)
Things to know:
Each student is expected to maintain a binder that will be graded regularly.
There will be a home assignment daily. If problems are assigned; all work must be shown.
Students will have 1 to 2 test or quizzes per week.
Unit assessments will be standardized and created by the Parish. It will follow the High School Comprehensive Curriculum.
Grades will be determined based on total points that your child earns during the grading period. The school grading scale is then used to determine the letter grade.
Class Schedule
1st period Duty
2nd period Algebra I
3rd period Algebra I
4th period Algebra I
5th period Algebra I
6th period Planning Period
7th period Algebra I
Attendance
Algebra I Attendance:
To achieve success in Mathematics, it is important for students to attend class regularly. Many students have great difficulty trying to learn Algebra work on their own after an absence. Class work tends to build on prior learning. If a student misses just one day, they have difficulty following new assignments. Attendance is taken at every class period. Students must bring a note from a parent for each day missed which explains the reason for the absence. Students have two days following an absence to make arrangements with a teacher to make up work. Most often, test make-ups are given after school and at the teacher's convenience.
East Baton Rouge Parish School System is an equal opportunity employer and does not discriminate on the basis of race, color, national origin, gender, age, or qualified disability.
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Mathematics
The Mathematics Division is committed to offering courses that allow students to satisfy and exceed school and state graduation requirements, as well as to build a rich understanding and appreciation of mathematics. Because math is vital to the development of thinking and questioning minds, the division offers opportunities for all students to discover and appreciate mathematical ideas. There are classes available to students of all abilities and grades, as well as opportunities to advance within the math sequence. Mathematics is vital to students leaving high school to enter college, the work force, or any future aspirations. Courses range from algebra through calculus, with statistics and computer science as additional options. The Mathematics Division wants to help students to stretch to their fullest potential, so that they can become independent learners, adept at using technology, and be comfortable in future mathematical endeavors.
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Reaching the Core of AS Mathematics
Reviews
The book includes student resource sheets and detailed teachers' notes. The supporting CD contains six computer programs which include help to reinforce and consolidate algebraic skills in the context of solving problems, and three 'big picture' programs that can be used in many different ways.
The CD also contains all the student resource sheets. The pack includes whole-class and group activities which encourage students to develop their understanding and enjoyment of mathematics, promote confidence and help with reasoning.
The resource is accessible to all students and will provide enrichment for - and extension to - the AS core.
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Robert A. McDougal
Teaching Statement
The typical undergraduate enters college with an unfortunate perception of mathematics, viewing it as a field with a fixed set of rules handed down from on high in the days of yore. Many students come to math classes expecting to receive magic formulas that will instantly bring them to the answer. It is my challenge and my joy as a math teacher to redirect my students' attention away from the final destination of an answer to the journey of reasoning that lies behind the solution.
I feel strongly about helping my students learn to reason mathematically because their
mathematical journey will ultimately lead them to the unknown. My engineering students hope to build new structures, new cars, and new technology. Many of the dynamics will be the same as in earlier technology, but each advance brings a new set of differential equations to describe the development. I can only cover a finite number of types of equations in class, but there are infinitely many questions waiting to be asked. The students who can reason for themselves are prepared to adapt to the new challenges and overcome any mathematical obstacles in their path.
It takes time and effort to shift students' thinking; I cannot simply tell them to go forth and understand. By getting my students actively engaged with the material, I can lead them to understanding. To this end, I promote self-study, class discussions, one-on-one discussions, and group cooperation.
I think the first steps toward understanding are best made outside of the classroom. My students know what problems will be assigned in advance, so I urge them to attempt the questions before coming to class. Some initially fear that struggling with unfamiliar problems is not an effective use of their time, but I challenge them to persevere, as those who make this extra effort are better prepared to face future variations on these problems.
Since many of my students have thought about the material before class, we are able to have lively discussions. I strongly support the old saying, "mathematics is not a spectator sport." By actively participating in class, my students ensure that they are on solid mathematical footing, because they have to be able to quickly make logical deductions. Promoting participation means far more to me than simply checking comprehension: as much as possible, I want my students to be engaged in the process of discovery. I want my students to view me not as an oracle but as a guide on their quest;
I ask my class "what if" questions to lead them toward the next theorem or result we need. When a student volunteers a formula from a different course, I ask the entire class to justify this formula before we proceed.
Keeping students actively involved in class keeps them coming back. Many mathematics classes have poor attendance because the students are bored - not inspired to think. Usually, students who skip class find themselves overwhelmed by the material, and their grades suffer. One of my classes in Autumn 2007 had every single student present the day I distributed course evaluations. Their final exams were a delight to grade, because their performance reflected their attendance and enthusiasm.
I encourage my students to continue their journey together even outside of the classroom. After they turn in their homework, I post my solutions online. I suggest they form study groups and discuss my approach, how it differs from theirs, and how their individual solutions differ. Much insight can be gained by contrasting alternative methods. I tell my students that even though I am their instructor, I still learn from seeing their work, so I know they can learn from each other.
At the end of the quarter, I ask my students to consider sharing their work with the entire class. Specifically, I pick out a number of problems and ask them to volunteer to write up one solution each. The response has been impressive; in Autumn 2007, my students gave me a total of 48 pages of solutions. Many no doubt sign up out of enlightened self-interest, because they want a large pool of sample problems. The creation of this resource is one of my goals as well, but I like this exercise because it motivates the students to think carefully about problems and write a clear presentation of their solutions.
Even when self-study, group-study, and class discussions are not sufficient, I strive to make sure no student falls by the wayside. I encourage my students to visit me during my office hours or talk to me before or after class. I am certainly happy when a student just wants to thank me for my presentation on series solutions to differential equations, but I urge them to let me know if my pace or my emphasis needs adjustment. Some students come to me with questions that they know are deep: one asked, "What do sinh and cosh mean?" That student and I discussed important qualities of functions in general, as well as the specific properties of hyperbolic trigonometric functions. Other students are more specific and just want to know where they made a mistake in a particular problem. I point out their mistakes, but then we discuss ways of catching errors before they become an issue.
I encourage many different paths toward understanding the course material, because I recognize that no two of my students are identical; each student learns in a way that is uniquely his or her own. Not everyone will be a math superstar when they leave my class, but I want everyone to be much closer to true understanding than when they started.
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Linear Algebra with Applications, CourseSmart eTextbook, 4th Edition
Description
Offering the most geometric presentation available, Linear Algebra with Applications, Fourth Edition emphasizes linear transformations as a unifying theme. This elegant textbook combines a user-friendly presentation with straightforward, lucid language to clarify and organize the many techniques and applications of linear algebra. Exercises and examples make up the heart of the text, with abstract exposition kept to a minimum. Extensive problem sets keep students involved in the material, while genuine applications for a broad range of sciences prepares them for the methods and models of contemporary scientists. In addition, the wealth and variety of exercise sets enable instructors to design a course to best suit the goals and needs of their students. This revision reflects careful review and appropriate changes to the wording of each idea, while preserving the content structure of the previous edition.
CourseSmart textbooks do not include any media or print supplements that come packaged with the bound book.
Table of Contents
1. Linear Equations
1.1 Introduction to Linear Systems
1.2 Matrices, Vectors, and Gauss-Jordan Elimination
1.3 On the Solutions of Linear Systems; Matrix Algebra
2. Linear Transformations
2.1 Introduction to Linear Transformations and Their Inverses
2.2 Linear Transformations in Geometry
2.3 Matrix Products
2.4 The Inverse of a Linear Transformation
3. Subspaces of R" and Their Dimensions
3.1 Image and Kernel of a Linear Transformation
3.2 Subspace of R"; Bases and Linear Independence
3.3 The Dimension of a Subspace of R"
3.4 Coordinates
4. Linear Spaces
4.1 Introduction to Linear Spaces
4.2 Linear Transformations and Isomorphisms
4.3 The Matrix of a Linear Transformation
5. Orthogonality and Least Squares
5.1 Orthogonal Projections and Orthonormal Bases
5.2 Gram-Schmidt Process and QR Factorization
5.3 Orthogonal Transformations and Orthogonal Matrices
5.4 Least Squares and Data Fitting
5.5 Inner Product Spaces
6. Determinants
6.1 Introduction to Determinants
6.2 Properties of the Determinant
6.3 Geometrical Interpretations of the Determinant; Cramer's Rule
7. Eigenvalues and Eigenvectors
7.1 Dynamical Systems and Eigenvectors: An Introductory Example
7.2 Finding the Eigenvalues of a Matrix
7.3 Finding the Eigenvectors of a Matrix
7.4 Diagonalization
7.5 Complex Eigenvalues
7.6 Stability
8. Symmetric Matrices and Quadratic Forms
8.1 Symmetric Matrices
8.2 Quadratic Forms
8.3 Singular Values
9. Linear Differential Equations
9.1 An Introduction to Continuous Dynamical Systems
9.2 The Complex Case: Euler's Formula
9.3 Linear Differential Operators and Linear Differential Equations
Appendix A. Vectors
Answers to Odd-numbered Exercises
Subject Index
Name
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Toughkenamon PrealgebraThe crucial skills gained in this course include analysis of numerical relations and spatial-visual understanding of graphing principles. The skills they learn in this course will stay with them throughout higher math education, and will prove useful in standardized testing, such as the PSAT and SAT. Pre-algebra centers on building the foundations of the student?s algebra.
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for College Students
A 4-color hardback book w/complete text-specific instructor and student print/"enhanced" media supplement package. AMATYC/NCTM Standards of Content ...Show synopsisA 4-color hardback book w/complete text-specific instructor and student print/"enhanced" media supplement package. AMATYC/NCTM Standards of Content and Pedagogy integrated in current, researched, real-world Applications, Technology Boxes, Discover For Yourself Boxes and extensively revised Exercise Sets. Early introduction and heavy "emphasis on modeling" demonstrates and utilizes the concepts of introductory algebra to help students solve problems as well as develop critical thinking skills. One-page Chapter Projects (which may be assigned as collaborative projects or extended applications) conclude each chapter and include references to related Web sites for further student exploration. The influence of mathematics in fine art "and their relationships" are explored in applications and chapter openers to help students visualize mathematical concepts and recognize the beauty in mathUnfortunately, this text was required for my class. I got to use the Lial series for PreAlgebra, and I will get to for Intermediate as well. They are much better for those who need more examples, description, worked problems, etc. This one assumes you know
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...Special integration techniques, including substitution, integration by parts and partial fractions are studied. After reviewing the basic concepts of Geometry, including lines, angles, and triangles, the focus of the course is proof. An essential concept is that of congruence, and methods of proving that triangles are congruent are introduced.
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Applied mathematics (minor subject)
An applied mathematician works with solving problems which lie beyond the realm of regular mathematics, and therefore Applied mathematics is the programme for you if you want to work with mathematics and still keep in mind how mathematics can be of use in your future career.
Applied mathematics is not a particular branch of mathematics, but rather a way of working with mathematics. In the Applied mathematics programme, you will learn to create models of and solve problems from the practical world by utilising advanced mathematical tools.
The Applied mathematics programme gives you the opportunity to solve complex problems and to create new insight and recognition. Applied mathematics is for you if you want to learn to utilise advanced mathematical tools and computers to model, analyse and solve complex problems in the business sector or in research. An applied mathematician masters and is able to further develop the mathematical tools which have contributed to the development of the modern society of information.
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Active knowledge of mathematic numerical methods of solving frequent practical problems as a precondition of effective utilization of professional programs, to which these methods are includedInterpretation of numerical methods, implemented in widely-utilized CAD programs, is given. This course covers essential methods of solving both linear and nonlinear problems. Within each group, methods are classified according to their features and practical applicability. The comment is then centred on the well proven methods. For these methods, also the MATLAB source code is available in computer exercises.
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MAS100 Mathematics with Maple
In this course we learn to use a program called Maple, which is a very
powerful tool for solving problems in mathematics. Maple will also be
used, to varying extents, in many subsequent courses. In parallel with
learning Maple, we will review and extend some topics from A-level.
Using Maple we will be able to treat complex examples painlessly, look
systematically for patterns, visualize our results graphically, and
so gain new insights.
Each week, students will attend one lecture, one lab session, and one tutorial. Some lectures will cover aspects of Maple, but most learning of Maple will take place in the lab sessions. In tutorials, students will work on problems by hand.
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circleteam123
A circle is a simple shape of Euclidean geometry that is the set of points in the
plane that are equidistant from a given point, the centre. The distance between
any of the points and the centre is ...
Before talking about linear programming, I would like to tell you the meaning of
"linear". Linear is a Latin word which means pertaining to or resembling a line.
In mathematics, linear equation means ...
In linear algebra, real numbers are called scalars and relate to vectors in a vector
space through the operation of scalar multiplication, in which a vector can be
multiplied by a number to produce ...
Are you anxious about your math skills or face difficulty while solving maths
problems, then online free math help is provided for you by various free online
math tutoring websites. Because of online ...
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Elementary Geometry For College Students - 5th edition
Summary: Building on the success of its first four editions, the Fifth Edition of this market-leading text covers the important principles and real-world applications of plane geometry, with a new chapter on locus and concurrence and by adding 150-200 new problems including 90 designed to be more rigorous. Strongly influenced by both NCTM and AMATYC standards, the text takes an inductive approach that includes integrated activities and tools to promote hands-on application and discovery.
Daniel C. Alexander has taught mathematics at Parkland College in Champagne, Illinois, for the past fifteen years. Prior to his arrival at Parkland, Professor Alexander taught at the high-school level. He received his undergraduate and graduate degrees at Southern Illinois, Carbondale.
Geralyn Koeberlein teaches mathematics at Mahomet-Seymour High School in Champagne, Illinois. She has been awarded several outstanding teacher awards throughout her 34 year career teaching at Mahomet-Seymour HS.
View Table of Contents
Note: Each chapter concludes with a Summary, Review Exercises, and a Chapter Test. 1. LINE AND ANGLE RELATIONSHIPS. Sets, Statements, and Reasoning. Informal Geometry and Measurement. Early Definitions and Postulates. Angles and Their Relationships. Introduction to Geometric Proof. Relationships: Perpendicular Lines. The Formal Proof of a Theorem. Perspective on History: The Development of Geometry. Perspective on Application: Patterns. 2. PARALLEL LINES. The Parallel Postulate and Special Angles. Indirect Proof. Proving Lines Parallel. The Angles of a Triangle. Convex Polygons. Symmetry and Transformations. Perspective on History: Sketch of Euclid. Perspective on Application: Non-Euclidean Geometries. 3. TRIANGLES. Congruent Triangles. Corresponding Parts of Congruent Triangles. Isosceles Triangles. Basic Constructions Justified. Inequalities in a Triangle. Perspective on History: Sketch of Archimedes. Perspective on Application: Pascal's Triangle. 4. QUADRILATERALS. Properties of a Parallelogram. The Parallelogram and Kite. The Rectangle, Square, and Rhombus. The Trapezoid. Perspective on History: Sketch of Thales. Perspective on Application: Square Numbers as Sums. 5. SIMILAR TRIANGLES. Ratios, Rates, and Proportions. Similar Polygons. Proving Triangles Similar. The Pythagorean Theorem. Special Right Triangles. Segments Divided Proportionally. Perspective on History: Ceva's Theorem. Perspective on Application: An Unusual Application of Similar Triangles. 6. CIRCLES. Circles and Related Segments and Angles. More Angle Measures in the Circle. Line and Segment Relationships in the Circle. Some Constructions and Inequalities for the Circle. Perspective on History: Circumference of the Earth. Perspective on Application: Sum of the Interior Angles of a Polygon. 7. LOCUS AND CONCURRENCE. Locus of Points. Concurrence of Lines. More About Regular Polygons. Perspective on History: The Value of Perspective on Application: The Nine-Point Circle. 8. AREAS OF POLYGONS AND CIRCLES. Area and Initial Postulates. Perimeter and Area of Polygons. Regular Polygons and Area. Circumference and Area of a Circle. More Area Relationships in the Circle. Perspective on History: Sketch of Pythagoras. Perspective on Application: Another Look at the Pythagorean Theorem. 9. SURFACES AND SOLIDS. Prisms, Area, and Volume. Pyramids, Area, and Volume. Cylinders and Cones. Polyhedrons and Spheres. Perspective on History: Sketch of Rene Descartes. Perspective on Application: Birds in Flight. 10. ANALYTIC GEOMETRY. The Rectangular Coordinate System. Graphs of Linear Equations and Slope. Preparing to do Analytic Proofs. Analytic Proofs. Equations of Lines. Perspective on History: The Banach-Tarski Paradox. Perspective on Application: The Point-of-Division Formulas. 11. INTRODUCTION TO TRIGONOMETRY. The Sine Ratio and Applications. The Cosine Ratio and Applications. The Tangent Ratio and Other Ratios. Applications with Acute Triangles. Perspective on History: Sketch of Plato. Perspective on Application: Radian Measure of Angles. APPENDICES. Appendix A: Algebra review. Appendix B: Summary of Constructions, Postulates, and Theorems and Corollaries1439047901138.02 +$3.99 s/h
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Elizabeth Stapel: The primary developer of Purplemath and the author of its lessons is
Elizabeth Stapel. Though she now has a master's degree in mathematics, she never would have believed
while growing up that she would one day be a math teacher. In grammar school, her two worst subjects
were math and phys-ed ("physical education"). For her high-school years, her parents
sent her to a religious school where the prevailing philosophy seemed to be that women needed to
be married, not educated. (Yes, those kinds of places still exist.) Upon graduation, her parents
put her to work at their church and then at their religious business. After five years of barely
paying her, her parents finally had no further use for her and allowed her to try college, so she
enrolled at the local state school. One of her first classes covered early-high-school algebra.
Ms. Stapel quickly discovered that, though she often
found math to be difficult, she had a taste for the subject. She started helping fellow students
through the university's tutoring service, later becoming a grader for the math department. While
grading homework for many professors' classes, she observed common problems that students have
and common mistakes that they make. When she tutored, she again encountered these areas of difficulty,
and was able to learn which techniques generally helped the students to succeed. These techniques
were often those that Ms. Stapel had used to conquer her own confusion when earlier taking these
same classes herself.
As a graduate student, Ms. Stapel worked in various
tutoring and teaching capacities, and learned to incorporate her success techniques into her instruction.
These are the same tips and techniques that she weaves through her in-class instruction and the
Purplemath lessons.
Her basic philosophy regarding algebra is "If
I can do this stuff, then so can you!"
History of Purplemath: Purplemath began in 1998 as a personal web site created by Elizabeth
Stapel. Ms. Stapel's initial site included course-specific materials for her math students. Later,
she started adding a few lessons. As she created more lessons, traffic at her personal site increased.
Eventually, she decided to do a complete site redesign
to create a more professional appearance and to highlight the list of lessons. In order to pick
a color theme, she asked her son, then about two and a half years old, which color he liked best. Naturally,
he picked purple.
Traffic continued to increase, and in 1999 the site
had to be moved from its free hosting to its own domain name. The name "Purplemath" was
chosen and registered. A few years later, "Purplemaths" (with an "s" at the
end) was added for the benefit of British-English speakers.
According to Quantcast,
Purplemath served about six million pageviews to nearly two
million unique visitors in September
of 2012. During the North-American school year, Purplemath uses as much as 600
gigabytes of bandwidth
in a month, serving as many as three hundred fifty thousand pageviews in
one day to more than one hundred forty thousand unique visitors. (Fewer
pages are served during the North-American summer break.) The average visitor comes to Purplemath directly from a search engine and reads
three topic-specific content pages.
Recognition: Thousands of sites are now linked to Purplemath, and thousands of visitors come
to the site each day. Purplemath has been listed as an online resource in such books as Cliffs
Quick Review: Algebra II. In addition, the following awards and notations have been made:
Chosen as one of HowToLearn.com's top three "Best Educational
Websites for Algebra", February 2012
Awarded third place in She Knows national poll, October
2010
Referenced in The New York Times, August 2010
Added to Schoolzone's webguide of recommended sites, January
2009
Included in Homeschool.com's "Top 100" Web sites list,
January 2008
Featured "Web Byte" in the NCTM news bulletin,
September 2006
Included in the listing of "Net Goodies" in the NADE
"Math SPIN News" journal, January 2006
Included in T.H.E. Journal's listing of General Math Resources,
July 2005
Listed as a TechLearning "Site of the Day", February 2005
Featured in the
Webwatch column in "The Telegraph"
newspaper of Calcutta, India, 16 February 2005
Added to EEVL's Mathematics
listings, February 2005
Added to Homeschool.com's "Top 100" Web Sites
list, September 2004
Rated by Education World as an "A+" site, October 2003
Added to the Internet Scout Report's archive of educational
resources, June 2003
Included in the Eisenhower National Clearinghouse's
Digital Dozen, April 2003
Added to Kathy Schrock's Guide for Educators,
April 2003
Listed as a Links2Learning "Premier Page",
April 2002.
Selected as an Education Planet "Top Math
Site", February 2002.
Listed as a PBS "Recommended Site",
January 2002.
Mentioned in Wall Street Journalarticle, November 2001.
Chosen as a Learning in Motion "Top Ten Selection",
October 2001.
Listed as an Internet Web Guide Magazine "Molecule
of the Month" site, May 2001.
Placed on the "Top20" list for algebra,
September 2000.
Listed as the Math Goodies newsletter "Site
of the Month", August 2000.
Received the "Web Site Excellence Award"
from The School Page, March 2000.
Purplemath is frequently referenced by About.com,
GoogleAnswers, and Wikipedia; and many
have written
to thank Purplemath for the help it provides.
Software used in development: Many have inquired about the software used to create the various graphics
on Purplemath. Graphs usually begin their life in the Equation Grapher program,
produced by MFSoft International. Screen-captures are taken from graphing calculators using
the Texas Instruments' TI Connect software.
Other graphics are created, and graphs are "tweaked", inside Paint Shop Pro, now
owned by the Corel Corporation. The animations are also created in Paint Shop Pro, through the
Animation Shop plug-in. Mathematical typesetting is done with MathType, produced
by Design Science.
Purplemath has no affiliation with one "Joshua
Schneider" (AKA "Josh Metnick"), "AIS, Inc"
(AKA "Chicago.com"),
"John
F Stapel" (AKA "Dr Stapel"),
or their various confederates. Their representations (claims of ownership
interest in, authorship of, affiliation with, or employment at Purplemath; offers to sell Purplemath;
etc) will not be honored. Apologies for any confusion.
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This material is based upon work supported by the National Science Foundation under Grant Number 9752485. The materials
were developed and assessed by Prof. Kelly Black (Mathematics),
Prof. Dawn Meredith (Physics) and Prof. Karen Marrongelle
(Mathematics), with help from many others. (Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. )
In this integrated course, the mathematical ideas are applied
to and motivated by the work in physics; this connection gives the
mathematics a rich context. But also, students'
understanding of physics is improved by the early and frequent
application of powerful ideas from calculus.
The term "studio" (initially used at Rensselear Polytechnic
Intsutite) is meant to indicate that student are actively working
in small during much of the class, that the lab portion of the
class is integrated into the class, and that the class activities
are based on the findings of education research. Other
universities using similar active learning formats are
RPI
and North Carolina State
University (follow the link to SCALE-UP).
On the menu bar at the left, there are links to some of our
materials in pdf format. The best place to start is the
instructor's manual which gives an overview of the course. There
are also slides from an overview of the course given to UNH
faculty in Fall 2001.
Next, we provide both brief and detailed schedules that show
how the physics and mathematics connected.
We also provide the classroom activities that we have
written. [The physics activities were also supplemented by
Tutorials in Introductory Physics by Lillian McDermott and
Peter Shaffer (Prentice Hall)]. Both courses used standard (not
reform) texts in their disciplines. Feel free to use these
activities in your classroom, either as is or modified; but we
would appreciate a little credit.
Finally, since one of our main goals in this course is
improving student problem solving abilities, we will soon provide
copies of our projects. These are real-world problems that
require mathematics and physics to solve, and were solved by our
students in groups, outside of class. We include a sample report
write-up and a sample grading scheme. Please note that there are
several other places to find non-trivial problems on the web,
including
University of Minnesota , University Of
Massachusetts at Amherst , and Carnegie Mellon University
If you have
calculus/physics materials that you would like to share, feel free
to send to me (Dawn
Meredith) an html file, pdf file, or web link that I can put
here.
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Each of the PowerPoint files below presents 10 problems that are similar in style and content to the COMPASS algebra test. The correct answers appear after the last question. Complete solutions to each problem are included after the answer slide.
You can access all of the files in the tables below with a regular left-click. However you may find that it is easier to copy the files to your computer rather than using the files while online. The links below are links to files that you can download to your own computer. Here is how.
Right-click the link you are interested in
Choose the option save target as
Select the location where you want the file to be saved.
Click OK.
Math COMPASS Worksheets
These worksheets are Word documents that contain 10 multiple choice practice questions. The answers are included at the end of the sheet. Try these problems before you use the PowerPoint solutions in the table below.
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Synopsis
From differentiation to integration - solve problems with ease Got a grasp on the terms and concepts you need to know, but get lost halfway through a problem or, worse yet, not know where to begin? Have no fear! This hands-on guide focuses on helping you solve the many types of calculus problems you encounter in a focused, step-by-step manner. With just enough refresher explanations before each set of problems, you'll sharpen your skills and improve your performance. You'll see how to work with limits, continuity, curve-sketching, natural logarithms, derivatives, integrals, infinite series, and more! 100s of Problems! Step-by-step answer sets clearly identify where you went wrong (or right) with a problem The inside scoop on calculus shortcuts and strategies Know where to begin and how to solve the most common problems Use calculus in practical applications with confidence
Found In
eBook Information
ISBN: 97804717627
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This study examined the effectiveness of four types of review sessions given the day before a unit exam. Over a three week period, four Algebra 1 classes were taught the same unit by the principal investigator. At the end ...
Due to steady increases in students being diagnosed with disabilities, schools have transitioned to becoming more inclusive. As a result, children with disabilities are receiving more instruction within the general education ...
In this experiment two classes received instruction on integer operations. The first received instruction with the use of technology and the second class was instructed through a traditional approach. The study progressedBone Morphogenetic Protein 1 (BMP 1) functions in normal embryological development. The goal of this research was to obtain the sequence of salamander BMPl. Following sequence determination, an in situ probe for BMPJ ...
We used radio telemetry to determine the distribution and movements of paddlefish Polyadon spathula in the Allegheny Reservoir. Thirty-one adult and subadult paddlefish collected from spring congregation areas in the ...
This paper discusses a study that solicited data from teachers within two small city school districts. The study resulted from a five year federal education grant whose main objective was to provide intensive training and ...
This study explores the connection between student understanding of arithmetic and algebra through the evaluation of numeric expressions and the simplification of structurally comparable algebraic expressions. It isThis study examines the types of mistakes that students make solving multi-step linear equations. During this study, students completed a 15-problem test containing different types of multi-step linear equations appropriate ...
Understanding the concept of mathematical variables gives an opportunity to expand and work on high-level mathematics. This study examined college students' comprehension of variables as well as variable use in well-known ...
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Unit specification
Aims
This module aims to engage students with a circle of
algorithmic techniques and concrete problems arising
in elementary number theory and graph theory.
Brief description
Modern Discrete Mathematics is broad subject bearing
on everything from logic to logistics. Roughly speaking, it
is a part of mathematics that touches on those subjects that
Calculus and Algebra can't: problems where there is no sensible notion
continuity or smoothness and little algebraic structure. The subject,
which is typically concerned
with finite or at the most countable sets of objects,
abounds with interesting, concrete problems and entertaining examples.
Throughout, we will be interested in developing and analysing
algorithms: explicit recipes to solve problems and
prove theorems.
Intended learning outcomes
Students should develop the ability to think and argue algorithmically,
mainly by studying examples in elementary number theory, graph theory and
combinatorics.
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Author's Description
Inverse Matrices - Mathematical program for university students.
Mathematical program for university students.
Inverse Matrices gives a step-by-step yet complete solution of the following problem: Given a 2x2, or 3x3, or 4x4, or 5x5 matrix. Find its inverse matrix by using the Gauss-Jordan elimination method. The program is designed for university students and professors.
In linear algebra an n-by-n (square) matrix A is called invertible or nonsingular or nondegenerate, if there exists an n-by-n matrix B such that AB = BA = In, where In denotes the n-by-n identity matrix and the multiplication used is ordinary matrix multiplication. If this is the case, then the matrix B is uniquely determined by A and is called the inverse of A, denoted by A−1.
Requirements:
- Internet Explorer 5.5 or later
Limitations:
- 7-day trial
- Nag screen
Inverse Matrices 1.04 is licensed as Trial for the Windows operating system / platform. Inverse Matrices is provided as a free to try download for all software users (Trial).
Related Searches
Inverse Matrices Dekov Software. Please be aware that we do NOT provide Inverse Matrices cracks, serial numbers, registration codes or any forms of pirated software downloads.
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Costs
Course Cost:
$300.00
Materials Cost:
None
Total Cost:
$300
Special Notes
State Course Code
02052Materials to be ordered via the DLD
Description
Algebra I students will deepen their conceptual understanding of key algebraic concepts, work toward computational fluency, and extend their knowledge of problem-solving applications.
Course topics include an Introductory Algebra review; measurement; an introduction to functions; problem solving with functions; graphing; linear equations and systems of linear equations; polynomials and factoring; and data analysis and probability.
Students are supplied with a scaffolded note-taking guide, called a Study Sheet, as well as a post-study Checkup activity, providing them the opportunity to hone their computational skills by working through low-stakes problem sets before moving on to a formal assessment.
Math is not all numbers. Accessible text supports students in comprehending academic math content. New vocabulary is supported with rollover definitions and usage examples that feature audio and graphical representations of terms.
To further assist students for whom language presents a barrier to learning or who are not reading at grade level, Algebra I includes audio resources in both Spanish and English.
The content is based on the National Council of Teachers of Mathematics (NCTM) standards and is aligned to state standards.
Literacy Advantage courses support academic success in standards-based high school courses for students who are reading below proficient. Literacy Advantage courses assist students in mastering required math, science, English, and social studies content to earn credits toward graduation, while simultaneously developing reading skills. Courses are based on the most current research in adolescent literacy and best practices for instruction and intervention. Each semester course offers 60–80 hours of interactive direct instruction, guided practice, and integrated formative, summative, and diagnostic assessment.
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Synopsis
A guide to the theory behind bond math formulas
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Department of Mechanical Engineering, Unit Catalogue 2008/09
ME10304 Mathematics 1
Credits: 6
Level: Certificate
Semester: 1
Assessment: CW 10%, EX 90%
Requisites:
Aims: This is the first of two first year units intended to lead to confident and error-free manipulation and use of standard mathematical relationships in the context of engineering mathematics. The unit will consolidate and extend topics met at A-level, so that students may improve their fluency and understanding of the basic techniques required for engineering analysis.
Learning Outcomes: After taking this unit the student should be able to:
Handle circular and hyperbolic functions, and sketch curves. Differentiate and integrate elementary functions, products of functions etc.. Use complex numbers. Employ standard vector techniques for geometrical purposes. Determine the Fourier series of a periodic function.
Skills: Numeracy; working independently.
Content: Elementary topics: curve sketching; hyperbolic and circular functions; roots of equations; identities; partial fractions; arithmetic and geometric progressions; binomial expansions. Differentiation: limit definition; notation; higher derivatives; standard derivatives; derivative of products and functions of functions; Taylor's series; partial differentiation. Integration: definition as an area; integration by substitution, using partial fractions; integration by parts; mean and RMS. Complex numbers: definition; geometric representation; modulus and argument; Cartesian and polar forms; Euler's formula; elementary operations; roots. Vectors: definition; components and unit vectors; scalar and vector products and their use; geometrical applications. Fourier Series: definition; interpretation; use of symmetries; convergence properties.
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Representations
Mathematical objects admit a variety of representations. Using multiple (graphical, verbal, tabular, algebraic) representations of a function can bring out hidden properties of the objects being considered. For example, the graphs of two intersecting, parallel, or coincident lines reveal why linear systems of equations may have a unique solution, none at all, or infinitely many. This course focuses on the real (number) line and coordinate systems in two and three dimensions, as systems for representing certain mathematical objects (real numbers and correspondences, including functions) and for modeling relations among quantities. The primary goal is exploring and increasing the understanding of algebraic and geometric representations in these systems. Teachers discuss selected examples from educational research to gain insight into students' reasoning about number lines, coordinate systems, and the mathematical objects they represent. Part-whole representations of fractions (pizza models) are critically assessed and contrasted with representations of fractions (1) on the real line and (2) in the plane. They are discussed as models of rational numbers as well as models of relations among physical quantities. Examples from educational research on students' understanding and misunderstandings about fractions and division (e.g. the belief that multiplication makes bigger, division makes smaller, etc.) are also studied.
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Calculus, Books a la Carte Edition
Description
Table of Contents
Chapter 1: Functions
1.1 Review of Functions
1.2 Representing Functions
1.3 Trigonometric Functions and Their Inverses
Chapter 2: Limits
2.1 The Idea of Limits
2.2 Definitions of Limits
2.3 Techniques for Computing Limits
2.4 Infinite Limits
2.5 Limits at Infinity
2.6 Continuity
2.7 Precise Definitions of Limits
Chapter 3: Derivatives
3.1 Introducing the Derivative
3.2 Rules of Differentiation
3.3 The Product and Quotient Rules
3.4 Derivatives of Trigonometric Functions
3.5 Derivatives as Rates of Change
3.6 The Chain Rule
3.7 Implicit Differentiation
3.8 Derivatives of Inverse Trigonometric Functions
3.9 Related Rates
Chapter 4: Applications of the Derivative
4.1 Maxima and Minima
4.2 What Derivatives Tell Us
4.3 Graphing Functions
4.4 Optimization Problems
4.5 Linear Approximation and Differentials
4.6 Mean Value Theorem
4.7 L'Hôpital's Rule
4.8 Antiderivatives
Chapter 5: Integration
5.1 Approximating Areas Under Curves
5.2 Definite Integrals
5.3 Fundamental Theorem of Calculus
5.4 Working with Integrals
5.5 Substitution Rule
Chapter 6: Applications of Integration
6.1 Velocity and Net Change
6.2 Regions Between Curves
6.3 Volume by Slicing
6.4 Volume by Shells
6.5 Length of Curves
6.6 Physical Applications
6.7 Logarithmic and Exponential Functions Revisited
6.8 Exponential Models
Chapter 7: Logarithmic and Exponential Functions
7.1 A Short Review
7.2 Inverse Functions
7.3 The Natural Logarithm
7.4 The Exponential Function
7.5 Exponential Models
7.6 Inverse Trigonometric Functions
7.7 L'Hôpital's Rule Revisited and Growth Rates of Functions
Chapter 8: Integration Techniques
8.1 Integration by Parts
8.2 Trigonometric Integrals
8.3 Trigonometric Substitutions
8.4 Partial Fractions
8.5 Other Integration Strategies
8.6 Numerical Integration
8.7 Improper Integrals
8.8 Introduction to Differential Equations
Chapter 9: Sequences and Infinite Series
9.1 An Overview
9.2 Sequences
9.3 Infinite Series
9.4 The Divergence and Integral Tests
9.5 The Ratio and Comparison Tests
9.6 Alternating Series
Review
Chapter 10: Power Series
10.1 Approximating Functions with Polynomials
10.2 Power Series
10.3 Taylor Series
10.4 Working with Taylor Series
Chapter 11: Parametric and Polar Curves
11.1 Parametric Equations
11.2 Polar Coordinates
11.3 Calculus in Polar Coordinates
11.4 Conic Sections
Chapter 12: Vectors and Vector-Valued Functions
12.1 Vectors in the Plane
12.2 Vectors in Three Dimensions
12.3 Dot Products
12.4 Cross Products
12.5 Lines and Curves in Space
12.6 Calculus of Vector-Valued Functions
12.7 Motion in Space
12.8 Length of Curves
12.9 Curvature and Normal Vectors
Chapter 13: Functions of Several Variables
13.1 Planes and Surfaces
13.2 Graphs and Level Curves
13.3 Limits and Continuity
13.4 Partial Derivatives
13.5 The Chain Rule
13.6 Directional Derivatives and the Gradient
13.7 Tangent Planes and Linear Approximation
13.8 Maximum/Minimum Problems
13.9 Lagrange Multipliers
Chapter 14: Multiple Integration
14.1 Double Integrals over Rectangular Regions
14.2 Double Integrals over General Regions
14.3 Double Integrals in Polar Coordinates
14.4 Triple Integrals
14.5 Triple Integrals in Cylindrical and Spherical Coordinates
14.6 Integrals for Mass Calculations
14.7 Change of Variables in Multiple Integrals
Chapter 15: Vector Calculus
15.1 Vector Fields
15.2 Line Integrals
15.3 Conservative Vector Fields
15.4 Green's Theorem
15.5 Divergence and Curl
15.6 Surface Integrals
15.6 Stokes' Theorem
15.8 Divergence Theorem
This title is also sold in the various packages listed below. Before purchasing one of these packages, speak with your professor about which one will help you be successful in your course.
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Sci-Plus 300 talking scientific calculator
Product features
Perform complex mathematical calculations with ease with the Sci-plus 300 talking scientific calculator. This large screened calculator announces when each button is pressed in a clear US English female voice, enabling you to perform scientific, statistical and trigonometric calculations easily. It also displays on screen numbers in 90 point font.
Product details
Silver casing with large, high contrast 8 digit LCD display
number buttons have white text on a black background in 53 point font
function buttons have white and yellow text on a black or blue background in 22 point font
long life internal lithium battery lasts approx. 80 hours on a full charge
can be used with or without speech function (if using speech, headphones must be used)
supplied with a UK power adaptor, ear phones and large print instructions (other formats available in request)
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Water Boiling at Everest - Periodic Table of Videos
Boiling water at various altitudes on the trek from Lukla to Everest Base Camp.
More videos about boiling water coming soon.
Nepal Flag:
Everest 8848:
More scenic clips from Brady's trip:
Special thanks to Buddhi Rai and Chandra Rai
Music by:
More chemistry at
Follow us on Facebook at
And on Twitter at
Prepositions - Arrive AT, ON, or IN?
Arrive at, on, or in a city? Arrive on, in, or at Monday? In this basic grammar lesson, I'll show you the right preposition to use with the verb "arrive". An important lesson for all English learners who are confused by prepositions. Watch the lesson, then take the quiz:Mathematics C1 May 2011 Q10b
Shaping Modern Mathematics: The 19th Century
The 19th Century saw the development of a mathematics profession with people earning their living from teaching, examining and researching and with the mathematical centre of gravity moving from France to Germany. A lot of the mathematics taught at university today was initiated at that time. Whereas in the 18th Century one would use the term mathematician, by the end of the 19th Century one had specialists in analysis, algebra, geometry, number theory, probability and statistics, and applied...
Probability
Calculus
Topics covered in the first two or three semesters of college calculus. Everything from limits to derivatives to integrals to vector calculus. Should understand the topics in the pre-calculus playlist first (the limit videos are in both playlists)
Algebra
Topics covered from very basic algebra all the way through algebra II. This is the best algebra playlist to start at if you've never seen algebra before. Once you get your feet wet, you may want to try some of the videos in the "Algebra I Worked Examples" playlist.
Arithmetic
The most basic of the math playlists. Start here if you have very little background in math fundamentals (or just want to make sure you do). After watching this playlist, you should be ready for the pre-algebra playlist.
Justice with Michael Sandel
Instructor Michael Sandel
JUSTICE is the first Harvard course to be made freely available online and on public television. Nearly a thousand students pack Harvard's historic Sanders Theatre to hear Michael Sandel, "perhaps the most prominent college professor in America," (Washington Post) talk about justice, equality, democracy, and citizenship.Iain Banks, in conversation with The Open University (full)
Free learning with The Open University
---
Author Iain Banks talks to Open University Lecturer in Creative Writing Derek Neale about the digitisation of books, his writing process, the impact of world events on his work and much more.
(Full)
---
Interview also available as audio only
Study 'Creative writing' with the OU
MIT 9.00SC Introduction to Psychology, Fall 2011
View the complete course:
Instructor: John Gabrieli
Introduction to Psychology
License: Creative Commons BY-NC-SA
More information at
More courses at h 21L.011 The Film Experience, Fall 2007
View the complete course:
Instructor: David Thorburn
This introduction to narrative film emphasizes the evolution of the film medium and the intrinsic artistic qualities of individual films. The selected lectures in this video collection cover early cinema & silent films, the 1970s, and neorealism.
License: Creative Commons BY-NC-SA
More information at
More courses atYour Mass is NOT from Higgs Boson
The Higgs Boson is awesome but it's NOT responsible for most of your mass! Thanks to audible.com for supporting this episode:
The Higgs mechanism is meant to account for the mass of everything, right? Well no, only the fundamental particles, which means that electrons derive their mass entirely from the Higgs interaction but protons and neutrons, made of quarks, do not. In fact the quark masses are so small that they only make up about 1% of the mass of the proton (and a ...
The True Science of Parallel Universes
Oh, Hey! MinuteEarth! .........and you can also subscribe to MinutePhysicsDrums by Jason Burger
Who was the REAL Good Will Hunting? - Numberphile
George Dantzig, William Sidis, Srinivasa Ramanujan? Who was the real Good Will Hunting?
Maths in Good Will Hunting:
This video features Numberphile's very own mathematics superstar - Dr James Grime.
Website:
Numberphile on Facebook:
Numberphile tweets:
Google Plus:
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Videos by Brady Haran
A r...
Jetpack Rocket Science
Check out 2Veritasium!
MinutePhysics has a great video on Milkman, vomiting levitator:
Jetpacking was awesome fun! Despite the fat lip I had a great time. I think knowing a bit about physics actually helps fly the jetpack. It works on the same principle as a rocket (Newton's 3rd law) but unlike the shuttle, you don't carry your own propellant with you. Instead, water is pumped out of the lake by the jetski at up to 60 litres a second. It is then fi...
Why Do Venomous Animals Live In Warm Climates?
Subscribe to Veritasium - it's free!
As a Canadian-Australian, I have always wondered why it is that Australia has so many venomous animals that can kill you while Canada has virtually none. But it's not just Australia - it seems like all beautiful, warm places are cursed with venomous native species. So I set out to find the truth: why have all these venomous species evolved in the world's best holiday destinations?
I asked chemists, visited the zoo, interviewed entomo...
New Largest Known Prime Number - Numberphile
There is a new "largest known prime number".
Extra footage:
More on Mersenne Primes:
Perfect Numbers:
Googolplex:
Graham's Number:
This video features Dr Tony Padilla from the University of Nottingham.
Website:
Numberphile on Facebook: Astronomy Lectures by Professor Carolin Crawford
As Gresham Professor of Astronomy, Carolin Crawford delivers many public lectures a year within the City of London. These are all recorded and released on the Gresham College website: 8.01 Physics I: Classical Mechanics, Fall 1999
Instructor: Prof. Walter Lewin
This course features lecture notes, problem sets with solutions, exams with solutions, links to related resources, and a complete set of videotaped lectures. The 35 video lectures by Professor Lewin, were recorded on the MIT campus during the Fall of 1999. Prof. Lewin is well-known at MIT and beyond for his dynamic and engaging lecture style.
Find more lecture notes, study materials, and more courses at MIT 22.033 Nuclear Systems Design Project, Fall 2011
View the complete course:
Instructor: Dr. Michael P. Short
In this capstone design project course, students design a nuclear reactor that generates electricity, hydrogen and biofuels. Lectures introduce each major subsystem and explore design methods, and are followed by mid-term and final student presentations.
License: Creative Commons BY-NC-SA
More information at
More courses at 6.033 Computer System Engineering, Spring 2005
This We will also look at case studies of working systems and readings from the current literature provide comparisons and contrasts, a... 11.965 Reflective Practice, IAP 2007
View the complete course:
Instructor: Ceasar McDowell, Claudia Canepa, Sebastiao Ferriera
The course is an introduction to the approach of Reflective Practice developed by Donald Schön. It is an approach that enables professionals to understand how they use their knowledge in practical situations and how they can combine practice and learning in a more effective way. Through greater awareness of how they deploy their knowledge in practical situations, professio...
Currency
Sanusi Lamido Sanusi: Reforming Nigeria's Financial Sector
At first, banks in Nigeria were able to weather the global financial crisis. However, the second-round effects saw the collapse of prices on the stock market, credit contraction, and depletion of external reserves.
Sanusi Lamido Sanusi, governor of the Central Bank of Nigeria, as part of the Global Speaker Series at the Stanford Graduate School of Business, walks through the lessons learned from the crisis. Unlike European banks, Nigeria acted decisively in injecting capital to stabilize ban...
Alibaba's Ma Reflects On 12-Year Journey at China 2.0 Conference
Jack Ma, Chairman and CEO of Alibaba Group, delivered the closing keynote address at the conference "China 2.0: Transforming Media and Commerce", hosted by the Stanford Program on Regions of Innovation and Entrepreneurship (SPRIE) at the Stanford Graduate School of Business, on Sept. 30, 2011.
Related Links:
Rethinking Learning with Salman Khan
The Mastery in Communication Initiative and the Stanford GSB Education Club hosted Salman Khan, who spoke about the history and evolution of the Khan Academy and how it is reshaping the way people learn today.
Related Links:
Concise Storytelling for Leaders Workshop
JD Schramm, Stanford GSB lecturer in organizational behavior and director of the Mastery in Communication Initiative, presents this workshop specifically designed to help alumni speakers for the 40-Year-Strong anniversary celebration of the Public Management Program and the Center for Social Innovation to create a four-minute personal story of impact .
The workshop includes topics like how to get quickly to your point and how to inspire your audience. It also features case discussions h...
Cutting Greenhouse Gas Emissions: Perspectives from CaliforniaModerated by Professor Mar Reguant, Nichols discusses the new cap-and-trade system and the current thinking around regional and federal policies.
Ni...
Rob Reid: The $8 billion iPod
Comic author Rob Reid unveils Copyright Math (TM), a remarkable new field of study based on actual numbers from entertainment industry lawyers and lobbyists Ni...
How and Why We Read: Crash Course English Literature #1
In which John Green kicks off the Crash Course Literature mini series with a reasonable set of questions. Why do we read? What's the point of reading critically. John will argue that reading is about effectively communicating with other people. Unlike a direct communication though, the writer has to communicate with a stranger, through time and space, with only "dry dead words on a page." So how's that going to work? Find out with Crash Course Literature! Also, readers are empowered during th...
Trent Anderson: "I believe the war touches everyone."
What's the most important issue to you in this election, and why?
Trent, President of the College Republicans at Shippensburg University and a retired officer in the U.S. Army, thinks the war in Iraq is the most important issue in this election.
Upload your answer to this question and post it to youtube.com/cspan, where you can watch and rank other voter's videos, too.
[Learn French] [movie] Remember me.divx
Cameron Russell: Looks aren't everything. Believe me, I'm a model.TEDTalks is a daily video podcast of the best talks and performances from the TED Conference, where the world's leading thinkers and doers give the talk of their lives in 18 minutes (or less). Look for talks on Tech...
Departing Space Station Commander Provides Tour of Orbital Laboratory...
The Times and Troubles of the Scientific Method
UPDATE
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Calculus: Single VariableCalculus: Single Variable exhibits the same strengths from earlier editions including the Rule of Four, an emphasis on modeling, exposition that students can read and understand and a flexible approach to technology. The conceptual and modeling problems, praised for their creativity and variety, continue to motivate and challenge students. The fifth edition includes even more problems and additional skill-building exercises.Foundations: The 5th edition of the text provides students with a clear understanding of the ideas of calculus as a solid foundation for subsequent courses in mathematics and other disciplines.
Rule of Four: Encourages students with a variety of learning styles to expand their knowledge by presenting ideas and concepts graphically, numerically, symbolically, and verbally.
Balanced Approach: The authors understand the important balance between concepts and skills. As instructors themselves, they know that the balance that an instructor chooses depends on the students they have: sometimes a focus on conceptual understanding is best; sometimes more drill is appropriate. The flexibility of the Fifth Edition allows instructors to tailor the course to their students.
Student Understanding: Exposition written in a way that students can actually read and more easily understand.
Flexible approach to technology
New to This Edition
Expanded Skills and Practice: The 5th edition includes a number new of skill-building and practice exercises, as well as additional problems.
Updated Data and Models: References to dates, prices, and other time-bound quantities have been updated for contemporary applied examples, problems, and projects. For example, Section 11.7 now introduces the current debate on Peak Oil production, underscoring the importance of mathematics in understanding the world's economic and social problems.
New Projects: There are new projects in Chapter 1:Which way is the Wind Blowing?; Chapter 5: The Car and the Truck; Chapter 9: Prednisone; and Chapter 10: The Shape of Planets.
More Problems: 10% more "problem"-type questions now included in the test banks and instructor's manuals.
Chapter 4 Reorganization: This chapter has been reorganized to smooth the approach to optimization.
New ConcepTests: Promote active learning in the classroom. These can be used with or without clickers, and have been shown to dramatically improve student learning. Available in a book or on theweb at
Expanded Appendices: A new Appendix D introducing vectors in the plane has been added. This can be covered at any time, but may be particularly useful in the conjunction with Section 4.8 on parametric equations.CourseSmart (eBook)
CourseSmart goes beyond traditional expectations-providing you instant, online access to the textbooks you need at an average savings of 50%. To learn more go to: coursesmart.com.
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Resources for Instructors
Instructor's Manual to accompany Calculus: Single and Multivariable, 5th Edition
Instructor's Manual.
Printed Test Bank
Printed Test Bank access to electronic versions of the Instructor's Manual, the Instructor's Solutions Manual, additional projects, as well as other valuable resources.
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What should one teach to liberal-arts students who will take only one math course, and that because it's required of them?
The conventional answer: partialPartial
What should one teach to liberal-arts students who will take only one math course, and that because it's required of them?
The conventional answer: partial
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The focus of the study was to identify secondary school students' difficulties with aspects of linearity and linear functions, and to assess their teachers' understanding of the nature of the difficulties experienced by their students. A cross-sectional study with 1561 Grades 8–10 students enrolled in mathematics courses from Pre-Algebra to Algebra II, and their 26 mathematics teachers was employed. All participants completed the Mini-Diagnostic Test (MDT) on aspects of linearity and linear functions, ranked the MDT problems by perceived difficulty, and commented on the nature of the difficulties. Interviews were conducted with 40 students and 20 teachers. A cluster analysis revealed the existence of two groups of students, Group 0 enrolled in courses below or at their grade level, and Group 1 enrolled in courses above their grade level. A factor analysis confirmed the importance of slope and the Cartesian connection for student understanding of linearity and linear functions. There was little variation in student performance on the MDT across grades. Student performance on the MDT increased with more advanced courses, mainly due to Group 1 student performance. The most difficult problems were those requiring identification of slope from the graph of a line. That difficulty persisted across grades, mathematics courses, and performance groups (Group 0, and 1). A comparison of student ranking of MDT problems by difficulty and their performance on the MDT, showed that students correctly identified the problems with the highest MDT mean scores as being least difficult for them. Only Group 1 students could identify some of the problems with lower MDT mean scores as being difficult. Teachers did not identify MDT problems that posed the greatest difficulty for their students. Student interviews confirmed difficulties with slope and the Cartesian connection. Teachers' descriptions of problem difficulty identified factors such as lack of familiarity with problem content or context, problem format and length. Teachers did not identify student difficulties with slope in a geometric
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The course syllabus is a general plan for the course; deviations announced
to the class by the instructor may be necessary.
Text:Mathematics
for Elementary Teachers , first edition, and the accompanying Class Activities
manual by Sybilla Beckmann, published by Addison-Wesley. These can be purchased
from the UGA bookstore and other bookstores. Please
bring the activity manual to class.
Course topics: Visualization.
Angles. Geometric shapes and their properties. Constructions with straightedge
and compass. Transformation geometry: reflections, translations, rotations.
Symmetry. Congruence. Similarity. Measurement, especially length, area, and
volume. Converting measurements. Principles underlying calculations of areas
and volumes. Why various area and volume formulas are valid. Area versus perimeter.
The behavior of area and volume under scaling.
Course objectives:
To strengthen and deepen knowledge and understanding of measurement and basic
geometry and how they are used to solve a wide variety of problems. In particular,
to strengthen the understanding of and the ability to explain why various procedures
and formulas in mathematics work. To strengthen the ability to communicate clearly
about mathematics, both orally and in writing. To promote the exploration and
explanation of mathematical phenomena. To show that many problems can be solved
in a variety of ways.
Class work:
This class is part of your preparation as a professional. As a professional,
you should engage in collegial discussions about professional practice and you
should constantly seek to enhance and refine your professional knowledge. To
receive a full participation score, your work in class must consistently exhibit
several or all of the following:
interest in mathematical ideas
interest in different ways of approaching mathematical ideas
careful listening to different ways of solving a problem
careful evaluation of proposed methods of solution
attempts to connect the course material to your experiences with children
and teachers at schools
There will be regular homework assignments. I encourage you to work on homework assignments with your classmates. Of course,
you should always write your homework up on your own, using your own words to
express the ideas you have discussed with others. Do not allow anyone to copy
your work. When you discuss assignments with others, all partners should "give
and take" ideas.
Late homework will not be accepted.
Please consult with me as soon as possible if you are unable to hand in an assignment
due to an illness or emergency.
Writing Intensive Program:
This section of MATH 5030 is part of the Writing
Intensive Program. The Writing Intensive Program is designed to
help courses teach the writing process within various disciplines. Although
you have taken English courses on writing, and although these courses will help
you with all your writing, mathematical writing has its own special features.
In mathematics, we seek coherent, logical explanations, in which the
desired conclusion is deduced from starting assumptions. Our graduate assistant,
Peter Petrov, has been trained by the Writing Intensive Program to help you
learn to write good mathematical explanations. By participating in the Writing
Intensive Program we have also learned about ways to use writing to deepen your
understanding of the course concepts.
How your grade will be calculated:
We will grade all your work on a 5.25 point scale, and we will assign points
as follows:
# of points
description
characteristics
5.25 points
exemplary
work that could serve as a model for other students
5 points
very good
correct work that is careful and thorough
4 points
competent
good, solid work that is largely correct
3 points
basic
work that has merit but also has significant shortcomings
2 points
emerging
work that shows effort but is seriously flawed
0 points
no credit
no work submitted, or no serious effort shown
Grading criteria: We will determine your score on assignments
and tests by the extent to which your work meets the following criteria:
The work is factually correct, or nearly so, with only minor, inconsequential
flaws.
The work addresses the specific question or problem that was posed. It is
focused, detailed, and precise. Key points are emphasized. There are no irrelevant
or distracting points.
The work could be used to teach a student: either a child or another college
student, whichever is most appropriate.
The work is clear, convincing, and logical. An explanation should be convincing
to a skeptic and should not require the reader to make a leap of faith.
Clear, complete sentences are used. Mathematical terms and symbols are used
correctly. If applicable, supporting pictures, diagrams, and/or equations
are used appropriately and as needed.
The work is coherent.
Your grade will be based on tests, homework, and a comprehensive final exam. I expect to give 2 tests and 2 announced
quizes during the semester. I will calculate your course score using the following
percentages.
term tests, 20% each
40%
quizzes, 7% each
14%
class participation (please see criteria above under class work)
3%
homework
15%
final exam
28%
Makeup exams or quizzes will not be given. If an exam or quiz is missed due
to an illness or emergency, I will calculate a grade for the exam or quiz using
a relevant portion of the final exam.
I expect to assign letter grades as follows.
for scores from
up to
letter grade
4.6
5.25
A
4
4.6
B
3.5
4
C
2.5
3.5
D
below 2.5
F
Materials needed: Please
have a calculator available. Please bring your activity manual to class. You
may wish to have colored pencils or markers on hand since we will frequently
solve problems with the aid of pictures.
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Mt 322 Topics in Geometry - Fall 2003
Course Description
The most important objective of this course is to introduce students
to mathematical thinking and reasoning through a hands-on exploration of
interesting and challenging topics in geometry.
The emphasis in this course is on
conjecture, exploration, and articulation of geometric ideas,
leading to the development of a robust proof or refutation.
Study Guides for Tests
Study guides for each test will be posted one week before each
scheduled test.
Study Guide for Benchmark Test #1
The window-of-opportunity for this benchmark
is September 16 - 26.
Study Guide for Test #1 is available.
This test will be given in class on September 30.
By class consensus, we rescheduled Test #2 to
Thursday, October 30. The study guide for this test is now available.
Study Guide for Test #3 is available.
This test has been rescheduled to Tuesday, November 25.
Study Guide for Benchmark Test #2
is available. The window-of-opportunity for this benchmark
is December 1 through December 8.
Make an appointment with Sister Barbara to take
the Benchmark outside of class time during this window-of-opportunity.
Study Guide for the Final Exam
is now available.
The cumulative final exam for this course is scheduled for
Thursday, December 11, 10:30 a.m. - 12:30 p.m.
Return to Sr. Barbara E. Reynolds
Home Page.
Return to
course list
for 2003 -- 2004 December 2, 2003.
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Algebra for College Students is designed to provide students with the algebra background needed for further college-level mathematics courses. The unifying theme of this text is the development of the skills necessary for solving equations and inequalities, followed by the application of those skills to solving applied problems. The primary goal in writing the third edition of Algebra for College Students has been to retain the features that made the second edition so successful, while incorporating the comments and suggestions of second-edition users. As always, the author endeavors to write texts that your students can read, understand, and enjoy, while gaining confidence in their ability to use mathematics. While the essence of the text remains, the topics have been rearranged to reflect the current needs of instructors and students.
Stock Availability:
This title will be ordered from the publisher. Usually ships in 10 - 15 days. Publisher may be out of stock in which case we will advise you. Allow a few extra days for delivery.
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Prepared by Martha Olney of the University of California, Berkeley, each chapter in this guide begins with an overview and is followed by a set of matching exercises and multiple-choice questions under Basic Definitions. These are followed by one set of exercises for students to undertake the Manipulation of Concepts and Models and a second set for the Applying the Concepts and Models. This is followed by some problems for Explaining the Real World and a set of questions under the heading Possibilities to Ponder. Finally, answers and solutions are provided for all exercises and problems.
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The Goal Angle Problem - Ken Koedinger
Two solutions to the following problem: as you are running down a soccer field with the ball, when is the angle subtended by the goal at its maximum? There is also a sketch illustrating a construction used in one of the solutions (quadrature of the rectangle).
...more>>
GSP Files - Nate Burchell
This website includes GSP files that can be freely downloaded for educational use. The author has used these files in his classes to illustrate certain concepts in Precalculus, AP Statistics, and AP Calculus AB/BC.
...more>>
High School Geometry Lessons - Jeffrey P. Bannish
Narrated screencast lessons, most between seven and fifteen minutes long, created to accompany the McDougal Littell high school geometry textbook. Bannish explains theorems and concepts visually, and also works select textbook example problems, often
...more>>
JavaGSP! - Annie Fetter, the Math Forum
A short tutorial: everything you need to know to make your first JavaSketchpad page. A quick reference, then some other features, details, and considerations you might want to familiarize yourself with if you choose to incorporate Java GSP into some of
...more>>
JavaSketchpad Center - Key Curriculum Press
JavaSketchpad is software that lets you interact with or publish on the Internet sketches from The Geometer's Sketchpad, a Dynamic Geometry exploration environment for Macintosh and PC computers. JavaSketchpad can be used to share geometry work with people
...more>>
JavaSketchpad DR3 Gallery - Key Curriculum Press
JavaSketchpad is software that lets you publish sketches from The Geometer's Sketchpad on the Internet. If you have a Java-compatible Web browser, visit this demo gallery for some examples of JavaSketchpad in use: Centroid; Stereo Icosahedron; Hypercube;
...more>>
MathBits.com - Frederick and Donna Roberts
Devoted to offering fun, yet challenging, lessons and activities in high school/college level mathematics and computer programming to students and teachers. Includes Teacher Resources for Algebra, Geometry, Algebra 2, and Statistics; Finding Your Way
...more>>
MathBoy's Page - Pat Ballew
Miscellaneous math links and explanations, including Discovery Units, some about geometry and some about algebra, written using the Geometer's Sketchpad: triangle medians (with explanation); angle bisectors in a triangle; three tangents to a circle; ahematical Golf Sketches - Math Forum
This activity for studying reflections finds the direction to hit a golf ball to get it to bounce off several walls and into the cup (includes a construction of the solution). See also the introduction to this activity (from the Math Forum's 1996 SummerMathzone - Angelo Mingarelli, Carleton University
Mathzone features online calculus quizzes and exams, as well as one testing "everyday math." It also offers several downloadable programs, including a Javascript applet about the 3n+1 sequence, and a demo version of software that qualitatively plots polynomials
...more>>
Orthocenter - Paul Kunkel
What is significant about the orthocenter of a triangle? Why does it even have a name? This investigation was prepared for a geometry teachers' workshop. It includes a lesson handout in Word format and was written for use in a computer lab with the Geometer's
...more>>
Pascal's Triangle - Math Forum/USI
A Web unit designed to support workshops given by the Math Forum for the Urban Systemic Initiative (Philadelphia and San Diego). Read about the history of Pascal's triangle and learn to construct it; view illustrations of number patterns to be discovered;
...more>>
Pascal's Triangle: Number Patterns - Math Forum
Some history and an interactive exploration of number patterns and an exploratory Internet Web unit for elementary, middle school, and high school, with lessons, number pattern studies, and links to relevant sites on the Web.
...more>>
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Elementary Functions -- 22M:009:081
Fall 2006
This course includes in
one semester the essentials of analytic geometry, high school algebra, and
trigonometry needed for calculus. It is roughly equivalent to 22M:002 and
22M:005 compressed into one semester. Emphasis is on the role of functions and
analytic geometry. Topics include functions, coordinate systems; properties and
graphs of algebraic, trigonometric, logarithmic, exponential functions; inverse
trigonometric functions; and properties of lines, circles, and other conics. This
course is not intended for those learning graphing, logarithms, exponentials,
or trigonometry for the first time. Such students should take the
appropriate lower-level course or courses such as 22M:002 or 22M:005. Students
are encouraged to use the Math Tutorial Laboratory.
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Enables readers to apply the fundamentals of differential calculus to solve real-life problems in engineering and the physical sciences Introduction to Differential Calculus fully engages readers by presenting the fundamental theories and methods of differential calculus and then showcasing how the discussed concepts can be applied to real-world... more...
An accessible introduction to the fundamentals of calculus needed to solve current problems in engineering and the physical sciences I ntegration is an important function of calculus, and Introduction to Integral Calculus combines fundamental concepts with scientific problems to develop intuition and skills for solving mathematical problems related... more...
Differential and Integral Calculus, Volume 2 : "Unlike modern mathematicians who pursue their research apart from engineering or physical applications, Richard Courant was adverse to abstract theories and vague theorems. The topics covered in this set will provide the reader with a solid background to understanding the mathematics of heat... more...
"This is the perfect solid-as-they-come, timeless book on the calculus, and most likely it will never be surpassed in this domain." –Amazon Review This book is intended for anyone who, having passed through an ordinary course of school mathematics, wishes to apply himself to the study of mathematics or its applications to science... more...
Packed with practical examples, graphs, and Q&As, this complete self-teaching guide from the best-selling author of Algebra Demystified covers all the essential topics, including: absolute value, nonlinear inequalities, functions and their graphs, inverses, proportion and ratio, and much more.
more...
This Ebook is concerned with both the theory of the Kurzweil-Henstock integral and the basic facts on Riesz spaces. Moreover, even the so-called Šipoš integral, which has several applications in economy, is illustrated. The aim of this Ebook is two-fold. First, it can be understood as an introductory textbook to the Kurzweil-Henstock integral... more...
This book treats all of the most commonly used theories of the integral. After motivating the idea of integral, we devote a full chapter to the Riemann integral and the next to the Lebesgue integral. Another chapter compares and contrasts the two theories. The concluding chapter offers brief introductions to the Henstock integral, the Daniell integral,... more...
This textbook collects the notes for an introductory course in measure theory and integration. The course was taught by the authors to undergraduate students of the Scuola Normale Superiore, in the years 2000-2011. The goal of the course was to present, in a quick but rigorous way, the modern point of view on measure theory and integration, putting... more...
Many problems in science can be formulated in the language of optimization theory, in which case an optimal solution or the best response to a particular situation is required. In situations of interest, such classical optimal solutions are lacking, or at least, the existence of such solutions is far from easy to prove. So, non-convex optimization... more...
The subject of fractional calculus and its applications (that is, convolution-type pseudo-differential operators including integrals and derivatives of any arbitrary real or complex order) has gained considerable popularity and importance during the past three decades or so, mainly due to its applications in diverse fields of science and engineering.... more...
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Online Number Theory Tutoring
for All Grades
Our Online Number Theory Tutoring program is designed to help you get the desired grade by mastering the subject.
Number and Operations are an essential part of the study of Mathematics. A number is a quantity that is used in counting and measuring. The definition of the term number includes such numbers as zero, negative numbers, rational numbers and complex numbers. The study of Number and Operations involves understanding representations, relationships and number systems.
Rational Numbers
Irrational Numbers
Significant Figures
Sets
Indices
Polynomials
Imaginary Number
Complex Number
Matrices
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Sequences and Series
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Binomial Theorem
Ratio and Proportion
Whether you need Number Theory help or some quick assistance in understanding Number Theory questions before a test or an exam, our Number Theory tutors can help. Our tutors provide you with instant help, homework help and help with assignments in Number Theory.
We have Number Theory tutors who are experts in Number Theory across K-12 and beyond. Whatever your requirements are, the rigor and discipline of our tutor certification program will ensure that you get all that you want and more in your Number Theory tutor. Our tutors are familiar with the National and various State Standards required across grades in the US and other countries.
With our Online Number Theory Tutoring and Number Theory Homework help programs, studying the subject becomes easy and fun for students. Under the expert guidance of our tutors, students excel in Number Theory.
Click on your grade below to get a sample list of topics covered in that Grade for Number Theory. Please note that all tutoring programs will be customized for the individual.
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Please Note: Pricing and availability are subject to change without notice.
Thousands of students, teachers and schools are using Algebra World to get great results.
It provides a proven and dynamic learning environment that motivates students to succeed.
The major topics covered in Algebra World are: Expressions, Variables, Algebra Notation, Pattern Recognition, Integers, One Variable Equations, Two Step Equations, Ratio, Proportion and Percent, and Geometry. Each topic has a series of detailed lessons designed to teach key mathematical concepts. The lessons are followed by challenges in three skill levels that assess understanding of the subject and mathematical reasoning ability.
Presenting Concepts Has Never Been Easier
MathRealm understands that you are challenged each day to motivate and teach a wide range of students with a wide range of learning needs. You have a very demanding job. Algebra World will give you the tools to make your job easier.
Success in Various Learning Environments
Why do teachers incorporate Algebra World into their classrooms? Algebra World's highly visual and interactive presentations are perfect for classroom demonstrations. The visualization of concepts adds excitement to the learning process. Students today relate more to math ideas that are accompanied by graphics, color and sound.
Not only is Algebra World great for classroom demonstrations, it is also ideal for individual instruction! The eye-catching graphics and sound effects allow students to see and hear what is happening. This helps students to better understand the concepts.
Turn Passive Listeners into Active Learners
MathRealm's research showed that students are not as responsive to long narrations in software as they are to interactive visuals and audio effects that draw them into the program as active learners, rather than passive listeners.
Hands-on virtual manipulatives with limited text reading and immediate visual feedback will capture your students' attention and help them understand concepts, as well as develop logical reasoning.
Algebra World focuses on developing concepts with:
Learning Tools
Our learning tools draw students into a concept and encourage exploration.
Interactive Practice Problems
Scored practice problems provide students with immediate feedback. If a student is unable to solve a practice problem, the program shows how to solve it correctly, step-by-step.
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The activities in this book illustrate how the CellSheet Application can be used to investigate numerical data by using examples relevant to students, such as tracking their grades or calculating savi... More: lessons, discussions, ratings, reviews,...
The activities in this brief book have been created to help teachers incorporate the Transformation Graphing Software Application into Algebra 1 and 2 curricula. Topics covered include Line, Quadratic... More: lessons, discussions, ratings, reviews,...
TI InterActive! is a new product that enables high school and college teachers and students to easily investigate ideas in mathematics and science. The purpose of this workbook is to introduce algebra... More: lessons, discussions, ratings, reviews,...
This workbook provides high school students with activities from algebra to calculus that use Texas Instruments software TI InterActive! TI InterActive! is software for the PC that combines a word pro
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Engineering Math (ODE) Homework by pjmarron
Im taking an engineering course named Ordinary Differential Equations, and basically I don't understand any of the examples therefore not being able to do any of the problems in the textbook. So i have… (Budget: $30-$250 USD, Jobs: Mathematics)
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Book Description: The strength of Engineering Computation is its combination of the two most important computational programs in the engineering marketplace today, MATLAB® and Excel®. Engineering students will need to know how to use both programs to solve problems. The focus of this text is on the fundamentals of engineering computing: algorithm development, selection of appropriate tools, documentation of solutions, and verification and interpretation of results. To enhance instruction, the companion website includes a detailed set of PowerPoint slides that illustrate important points reinforcing them for students and making class preparation easier.
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Intermediate Algebra Graphs and Models
9780321416162
ISBN:
0321416163
Edition: 3 Pub Date: 2007 Publisher: Prentice Hall
Summary: The Third Edition of the Bittinger Graphs and Models series helps readers succeed in algebra by emphasizing a visual understanding of concepts. This latest edition incorporates a new Visualizing for Success feature that helps readers make intuitive connections between graphs and functions without the aid of a graphing calculator. In addition, readers learn problem-solving skills from the Bittinger hallmark five-step ...problem-solving process coupled with Connecting the Concepts and Aha! Exercises. As you have come to expect with any Bittinger text, we bring you a complete supplements package including MyMathLabtrade; and the New Instructor and Adjunct Support Manual. KEY TOPICS: Basics of Algebra and Graphing; Functions, Linear Equations, and Models; Systems of Linear Equations and Problem Solving; More Equations and Inequalities; Polynomials and Polynomial Functions; Rational Expressions, Equations, and Functions; Exponents and Radicals; Quadratic Functions and Equations; Exponential and Logarithmic Functions; Conic Sections; Sequences, Series, and the Binomial Theorem. MARKET: For all readers interested in Algebra321416162-3-0-3 Orders ship the same or next business day... [more]
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Differential Equations. This text provides the conceptual development and geometric visualization of a modern differential equations course while maintaining the solid foundation of algebraic techniques that are still essential to science and engineering students. It reflects the new excitement in differential equations as the availability of technical computing environments likeMaple, Mathematica, and MATLAB reshape the role and applications of the discipline. New technology has motivated a shift in emphasis from traditional, manual methods to both qualitative and computer-based methods that render accessible a wider range of realistic applications. With this in mind, the text augments core skills with conceptual perspectives that students will need for the effective use of differential equations in their subsequent work and study.
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The Skills Check is a short survey which should take you no more than 3 minutes to complete. Once you have completed the Skills Check we provide you with a personal learning plan targeted to your personal study needs and goals.
Basic mathematics skills resources
Use the Maths Skills ebook to help you refresh your mathematical skills for the science course you are studying. You may also find the Maths Skills ebook questions helpful, to check your understanding of the mathematics topics in the Maths Skills ebook.
Working with charts, graphs and tables toolkit - Try this toolkit if you are having difficulties working with numerical information. It is relevant for courses with small amounts of mathematical, scientific or technical content that still need you to work with charts, graphs and tables.
More charts, graphs and tables toolkit - This is helpful if you have some experience of interpreting numerical data and understand basic statistics, but are not fully confident in producing charts, graphs and tables.
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Other Information
2010 Course Handbook
TEP429: Mathematics in the Secondary School I
This unit provides an introduction to the secondary mathematics curriculum and its teaching. There are three main themes: understanding the central concepts of school algebra; teaching methods, including lesson planning and the role of technology in mathematics education; and practical and professional issues arising from students' concurrent Professional Experience (TEP401). Particular emphasis is given to learning and teaching mathematics in Years 7 to 10.
Please consult the Secondary TEP Guide for recommended prior studies.
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Algebra Calculators
This section features several algebra calculators designed to help you evaluate and solve common algebraic problems. Algebra is the branch of mathematics that deals with general statements of relations. Considered one of the main branches of pure mathematics, algebra uses symbols and letters to represent numbers and values to describe the relationships between.
The origins of algebra can be traced and seen as far back as the Babylonians. However, it was the Greeks, around the 3rd century, that started studying and expanding algebra at a more in depth level. Diophantus of Alexandria, the Alexandrian Greek mathematician, is often credited with being the first person to study and teach the field of algebra in a manner that resembles what we now know today. For this reason, he was given the nickname the "Father of Algebra".
Diophantus wrote a series of books called Arithmetica which consisted of 130 algebraic problems and also featured detailed solutions for each. The equations throughout these books are often referred to as the Diophantine equations and they have served as the foundation for several modern day algebraic equations such as the quadratic equation.
After Diophantus, the next notable figure in the history of algebra is Persian mathematician and astronomer Muḥammad ibn Mūsā al-Khwārizmī. His mathematical text, originally written in Arabic around AD 820, was called Al-Kitāb al-mukhtaṣar fī hīsāb al-ğabr wa'l-muqābala. The word algebra derives from the word "al-ğabr" in the title of this text. The full translation of the title is The Compendious Book on Calculation by Completion and Balancing and the text featured the first systematic solution of linear and quadratic equations. It is often debated that al-Khwārizmī deserves the title as the "Father of Algebra" but Diophantus is generally still given credit.
The whole of algebra can be broken down into the following more specific categories: elementary algebra, abstract algebra, linear algebra, universal algebra, algebraic number theory, and algebraic geometry. Elementary algebra is the basis for all of the more advanced forms and it is the first type of algebra taught in education to students with no more than basic math experience. Throughout elementary school, junior high, high school, and college, students are generally offered multiple different courses in algebra which get more advanced and in depth as they progress. You can find many great free math classes online.
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Presents the results on positive trigonometric polynomials within a unitary framework; the theoretical results obtained partly from the general theory of real polynomials, partly from self-sustained developments. This book provides information on the theory of sum-of-squares trigonometric polynomials in two parts: theory and applications. more...
Demystified is your solution for tricky subjects like trigonometry. If you think a Cartesian coordinate is something from science fiction or a hyperbolic tangent is an extremeexaggeration, you need Trigonometry DeMYSTiFieD , Second Edition, to unravel this topic's fundamental concepts and theories at your own pace. This practical guide eases you... more...
Part of the ''Demystified'' series, this book covers various key aspects of trigonometry: how angles are measured; the relationship between angles and distances; coordinate systems; calculating distance based on parallax; reading maps and charts; latitude and longitude; and more. more...
...CliffsQuickReview course guides cover the essentials of your toughest classes. Get a firm grip on core concepts and key material, and test your newfound knowledge with review questions. CliffsQuickReview Trigonometry provides you with all you need to know to understand the basic concepts of trigonometry — whether you need a supplement to your... more...
Most math and science study guides are a reflection of the college professors who write them-dry, difficult, and pretentious.
The Humongous Book of Trigonometry Problems is the exception. Author Mike Kelley has taken what appears to be a typical t more...
Trigonometry has always been an underappreciated branch of mathematics. It has a reputation as a dry and difficult subject, a glorified form of geometry complicated by tedious computation. In this book, Eli Maor draws on his remarkable talents as a guide to the world of numbers to dispel that view. Rejecting the usual arid descriptions of sine, cosine,... more...
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This course is designed to strengthen and develop skills that are essential for students who will be entering an Algebra I course in the fall. We will study strategies for problem solving, patterns and functions, probability, graphing, equations, properties, exponents and geometric thinking. During the six-week course, we will identify individual student curricular needs then design instruction to challenge all students in the class. Students will approach problem solving using a scientific approach defining the problem, making predictions and hypotheses, testing assertions, using algebra to generalize from specifics, making conclusions and supporting them with logical argument and proof. This class is for students who have not taken Algebra I.
Grade requirements: For students completing Grade 7 or 8 in June 2013.
Homework per class meeting: 2-4 hours
Tuition: $650
SD3340
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8:30 AM – 12:00 PM
Claudia Benedetti
Accepting Applications
Algebra I
This six-week course covers a full year of Algebra I and is aligned with state and NCTM standards for high school Algebra classes. Topics to be covered include data organization; patterns and graphs; writing and solving equations; numeric, geometric, and algebraic ratios; slopes and rates of change; linear functions; factoring quadratics; graphing and systems of linear and nonlinear equations, area and sub problems; radicals and inequalities; exponents and quadratics; rational and irrational numbers; and quadratic functions. Students spend at least eight hours outside of class preparing for each class session. The atmosphere of the class is cooperative; the emphasis is on working together.
Prerequisite: Completion of Pre-Algebra, grade of A in current math class, Teacher Recommendation Form completed by current math instructor, and passing score on placement test.
Homework per class meeting: 4-6 hours
Tuition: $1000
SD3341
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Eli Lebow
Accepting Applications
Introduction to Geometric Thinking
This course is designed for students who want to preview selected topics from high school Geometry. The approach is informal, with hands-on activities that will allow students to explore geometric concepts. Through a variety of techniques such as cooperative learning, the discovery method, and model-making, students will learn about the major concepts of Euclidean geometry. Students will work on a number of special projects such as tessellations. This course will give students the confidence and background to perform well in the regular or honors Geometry courses at their schools in the fall.
Prerequisite: Completion of Algebra I.
Homework per class meeting: 2-5 hours
Tuition: $650
SD3343.1
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8:30 AM – 12:00 PM
David Carter
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SD3343.2
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1:00 PM – 4:30 PM
David Carter
Accepting Applications
Geometry
This fast-paced course completes all topics of first-year Geometry: points, lines, planes, and angles; deductive reasoning; parallel lines and planes; congruent triangles; quadrilaterals; inequalities in geometry; similar polygons; right triangles; circles; constructions and loci; areas of plane figures; areas and volumes of solids; coordinate geometry; transformations; and an introduction to trigonometry. Because the course covers a full year of Geometry, students spend at least eight hours outside of class preparing for each class session.
Prerequisite: Completion of Algebra I, grade of A in current math class, Teacher Recommendation Form completed by current math instructor, and passing score on placement test.
Homework per class meeting: 8-10 hours
Tuition: $1000
SD3344.1
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8:30 AM – 12:00 PM
Nakia Baird
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SD3344.2
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1:00 PM – 4:30 PM
Nakia Baird
Accepting Applications
Algebra II/Trigonometry
This extremely fast-paced course completes all topics of second-year Algebra with trigonometry: linear functions and relations; systems of linear equations and inequalities; quadratic functions and complex numbers; exponential and logarithmic functions; rational and irrational algebraic functions; quadratic relations and systems; higher degree functions and polynomials; sequences and series; graphing techniques; circular and trigonometric functions; and use of mathematical models for applications and problem solving. Because the course covers a full year of material, students spend a great deal of time outside class preparing for each class session.
Prerequisite: Completion of Geometry, grade of A in current math class, Teacher Recommendation Form completed by current math instructor, and passing score on placement test.
Homework per class meeting: 8-10 hours
Tuition: $1000
SD3345.1
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8:30 AM – 12:00 PM
Tobias Jaw
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SD3345.2
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1:00 PM – 4:30 PM
Tobias Jaw
Accepting Applications
Precalculus
This fast-paced course will cover topics necessary for success in Calculus: coordinate geometry including rational functions and their graphs; conic sections including rotation of axes; elementary functions including inverses and transformation theory; exponential and logarithmic functions; all topics from the trigonometry framework including polar coordinates, polar graphing, polar form of complex numbers, DeMoivre's Theorem, Trigonometric identities, triangle trigonometry for right triangles and non-right triangles, graphs of the trigonometric functions and their inverses; sequences, series, sigma notation; proof by mathematical induction; introduction to limits; and introduction to differentiation.
Prerequisite: Completion of Algebra II, grade of A in current math class, Teacher Recommendation Form completed by current math instructor, and passing score on placement test.
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Mathematics
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Summary: 95 Statistics is all around us, and Triola helps students understand how this course will impact their lives beyondthe classroomndash;as consumers, citizens, and profes...show moresionals.Elementary Statistics Using the TI-83/84 Plus Calculator, Third Edition provides extensive instruction for using the TI-83 and TI-84 Plus (and Silver Edition) calculators for statistics, with information on calculator functions, images of screen displays, and projects designed exclusively for the graphing calculator. Drawn from Triola's Elementary Statistics, Eleventh Edition, this text provides the same student-friendly approach with material presented in a real-world context.The Third Edition contains more than 2,000 exercises, 87% are new, and 82% use real data. It also contains hundreds of examples; 86% are new and 94% use real data. By analyzing real data, students are able to connect abstract concepts to the world at large, learning to think statistically and apply conceptual understanding using the same methods that professional statisticians employ.Datasets and other resources (where applicable) for this book are available here . ...show less
2010-02-18 Hardcover Very Good With disc. No underlining or highlighting. We ship all books within 24 hours of purchase. Books bought on weekend shipped first thing Monday morning.
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N/a Boston, MA 2011 Hard Cover Third Edition Fair 4to-over 9?"-12" tall. Text book has rough tears on top and bottom edges of cover. Corners are bumped. Includes CD. 865 pages. There is highlighting...show more throughout entire book. Some writing on a couple of the pages. Used sticker on spine and back cover. This includes the TI-84 calculator. ...show less
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Love Is the Answer Washington, DC
Access code for this book is sold separately and is NOT included. Hardcover w/unopened CD. Very clean; strong binding, no marks or highlighting
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Actually, I think it is rewarding to look some things up, even if you use Google and Co.. For a student it is also a psychological effect to find solutions on the Internet. Namely, if you have some problem in symplectic geometry courses, these problems are normally rather specific, so you will have trouble finding solutions on the web easily. However, when using Google books, you can easily find parts of books which may contain relevant information for your proof or even give a good starting point for a proof. If someone simply uses the Internet to copy a proof then he/she will have problems to really understand mathematics. But, admittedly, there are proofs that I haven't understood or, this more often the case, wouldn't be able to reproduce offhand. In this case, the internet proves to be very useful, especially if you also have students that try to autodidactically learn some further topics in mathematics.
Personally, I would design problem sheets as follows:
-Make 3 to 4 easy problems which simply consist of getting familiar with the definitions and the rules in the respective field.
-Then make one problem that is rather technical and requires the student to make some longer steps in proving the statement. These calculations shouldn't be too complicated as otherwise the student will probably lose patience and simply look the solution up.
-Then design 2-3 problems that are more far-leading and require using calculation rules, and a bit creativity. Still, they shouldn't be too complicated.
Why am i always telling you about the complexity of the problems? Well, at least in Germany, we have only 30% of the students obtaining a degree in mathematics. I don't know how things are handles in the U.S. or elsewhere, but most of our students are frustrated becuase they simply don't find a starting point for the exercises. And this shouldn't happen.
I think, most of the students have the will to solve problems on their own. Especially mathematics and physics are subjects you study because you're passionate about them. Biological research has shown indeed that motivated apes are more thankful and curious then demotivated apes. I think this applies to students as well (and to us as well). The typical student involved in a biologically complicates process. The post-adolesence. The years 15-30 are the years where you are requires to pass a lot of tests. And for doing so you have to be motivated and self-confident. At least in Germany, for a lot of students, this is a problem (But I don't think it's much different elsewhere, at least I hope so, because otherwise, we're doing something wrong here).
Most cheating can be avoided if questions are motivating and asked in sch a manner that the first ones are easy to answer, and the following ones increase slightly in diffculty.
This is my opinion. I talk to a lot of students in physics which suffer from depressions because they believe they won't get anything. This belief is apparenbtly that deep that they simply copy homework or use Google. Mostly, when these students continue their studies they are very succesful later on. But a lot of them simply stops studying math and physics. A lot of potential is wasted here.
All I've written may sound a bit offtopic, but I think that there is the real problem. If you motivate students to think on their own, they will rejoice in proofs and all that. This was also my (personal) experience.
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Autograph is the only software to let you visualise maths in 2D and 3D with ease. There are no arcane commands to learn - just point and click. Left click to select an object and right click for a context sensitive menu of mathematical actions. With Autograph, it's just you and the maths - free to go wherever enquiry takes you!
Optionally control Autograph from an iPad or Tablet PC wirelessly as you roam the classroom.
See a video of The Perse School, Cambridge, using Autograph this way.
Secret Weapons ...
Autograph has three secret weapons to give you complete control.
Slow Plot: the essential tool for "what happens next?"
Dynamic Constant Controller: see changes on the fly, with steps
Dynamic Animation Controller: brings maths to life
Easily import data, represent it in Autograph, then export to Word or Web
There's lots of educationally useful UK and world data on the Autograph website, but you can import data from anywhere on the web, or from Excel for instance, directly into Autograph by simple copy and paste.
Represent, manipulate and analyse your data dynamically in Autograph with mathematical rigour and precision - proper histograms are offered for example, with variable class interval widths - then copy and paste into Word documents to print and share, or save it as a web page.
Getting Going with Autograph
To get started with Autograph, you might like to take a look at some short videos in the Videos and Resources sections which will show you Autograph in action.
If you'd prefer to concentrate on learning your way around Autograph's interface, then here's a good video about the Standard Level of operation for starters, and some excellent Getting Going videos at the start of the Autograph Video Tutorial series here.
Use Photos or Images as backgrounds to bring STEM topics to life
Now you can bring maths to life with photos and images as your background. Import any graphic image, adjust the opacity so you can see your graphed model clearly, and fit functions to natural phenomena - whether it be fitting a quartic through five points to find the equation of an arch, or the trajectory of a projectile, or geometric features of architecture. A great way to relate maths to real world phenomena and engage attention. In Autograph 3.3, image handling has been improved: you can paste or drag image files into Autograph, and you can drag images straight off Firefox pages.
Geometry has been expanded, with
new angle measurement tools and marking. Text annotation is now dynamic
too. There's a dockable results box, tabbed workspaces and a redesigned
and expanded Help and Training system and more! In Autograph 3.3, many of the routines have been fine-tuned and operation is smoother.
There is a superb new "Save to Web" facility. Autograph activites can be quickly created and saved to HTML (eg for use in a VLE or Wiki). Anyone opening such an activity for the first time in Internet Explorer, Firefox or Safari will automatuically download the Autograph Player (which is installed anyway for all Autograph users).
All six 'Extras' have been completely re-written in stunning "Flash".
The multi-lingual interface has been extended to 18 languages, including the world's first true right-to-left Arabic notation.
The use of Autograph on Thin Client systems has been enabled.
Autograph is now activated online, enabling the smooth continuation of use for trial users, and greatly simplifying the process of delivering the software to students on the popular Extended Licence.
It is understood that many will want to take the opportunity to upgrade their licence to the popular Extended Licence to take advantage of the online activation.
Autograph 3.3 on the Mac
Download the Mac free trial. Autograph 3.3 now runs seamlessly on all Intel-based Apple Mac computers, including Mountain Lion. All the features of the PC version have been implemented (*) and AGG files will be fully interchangeable between the two systems.
Where possible the Mac interface has been adopted, so Ctrl-Click gives a Right-Click. The CTRL key is otherwise affected by the APPLE (command) key/
(*) The Save to Web feature has only been partially
implemented for MAC browsers; however this feature will
be fully available in a future release of the MAC version.
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Math 5 - Trigonometry Syllabus – Section 3386 - Fall '12
CATALOG COURSE DESCRIPTION: This course is the first of a two semester sequence preparing students for Calculus. In this course you will study functions with an emphasis on the trigonometric functions along with topics in analytic geometry. Topics will include a review of plane and coordinate geometry, functions, including function notation, transformations and inverses, definitions and graphs of the trigonometric functions, modeling periodic behavior, solving triangle problems with the Laws of Sines and Cosines, the conic sections, including an introduction to parametric and polar equations.
CALCULATORS: You may be restricted to a scientific calculator or no calculator on some tests.
EXAMS: There will be at least five chapter tests and a cumulative final exam. There may also be several projects, as circumstance demands. The point of these is to provide an opportunity to demonstrate your understanding of the concepts covered. As such, exam problems won't consist entirely of very familiar homework problems.
Teaching and Learning:
According to George Polya, we can articulate three major principles of learning (which governs teaching):
1. Active Learning. It has been said by many people in many ways that learning should be active, not merely passive or receptive; merely by reading books or listening to lectures or looking at moving pictures without adding some action of your own mind you can hardly learn anything and certainly you cannot learn much.
There is another often expressed (and closely related) opinion: The best way to learn anyting is to discover it by yourself. Lichtenberg (an eighteenth century German physicist, better known a s a writer of aphorisms) adds an interesting point:
"What you have been obliged to discover by yourself leaves a path in your mind which you can use again whn the need arises."
Less colorful but perhaps more widely applicable, is the following statement:
"For efficient learning, the learner should discover by himself as large a fraction of the material to be learned as feasible under the given circumstances."
This is the principle of active learning (Arbeitsprinzip, in German) It is a very old principle: it underlies the idea of "Socratic Method."
2. Best Motivation. Learning should be active, we have said. Yet the learner will not act if he has no motive to act. He must be induced to act by some stimulus, by the hope of some reward, for instance. The interest of the material to be learned should be the best stimulus to learning and the pleasure of intensive mental activity should be the best reward for such activity. Yet, where we cannot obtain the best we should try to get the second best, or the third best, and less intrinsic motives of learning should not be forgotten.
For efficient learning, the learner should be interested in the material to be learned and find pleasure in the activity of learning. Yet, beside these best motives for learning, there are other motives too, some of them desirable. (Punishment for not learning may be the least desirable motive.)
Let us call this statement the principle of best motivation.
3. Consecutive phases. Let us start from an often quoted sentence of Kant: "Thus all human cognition begins with intuitions, proceeds from thence to conceptions, and ends with ideas." The English translation uses the terms "cognition, intuition, idea." I am not able (who is able?) to tell in what exact sense Kant intended to use these terms. Yet I beg your permission to present of Kant's dictum:
Learning begins with action and perception, proceeds from thence to words and concepts, and should end in desirable mental habits.
To begin with, please, take the terms of this sentence in some sense that you can illustrate concretely on the basis of your own experience. (to induce you to think about your personal experience is one of the desired effects.) "Learning" should remind you of a classroom with yourself in it as student or teacher. "Action and perception" should suggest manipulating and seeing concrete things such as pebbles, or apples, or Cuisenaire rods; or ruler and compasses; orinsturments in a laboratory; and so on.
These principles proceed from a certain general outlook, from a certain philosophy, and you may have a different philosophy. Now, in teaching as in several other things, it does not matter much what your philosophy is or is not. It matters more whetner you have a philosophy or not. And it matters very much whether you try to live up t your philosophy or not . The only priniciples of teaching which I thoroughly dislike are those to which people pay only lip service.
Problem Solving: Much of the course is centered around applying these definitions and theorem by solving problems. The basic outline for general problem solving devised by Polya is a four step program:
1. Understand the problem
2. Devise a plan for solving the problem
3. Carry out the plan
4. Look back
HOMEWORK: Read the text, keep up with the assigned problems (as a minimum) and prepare questions about what you're learning for participation in class. You can expect to learn far more trigonometry individually or in small groups doing homework than you do in class. If you complete (and thoroughly understand) the homework assignment for each section, you will be well prepared to solve questions on tests and quizzes. At the beginning of each class, I will answer as many questions over the previous night's homework as time allows. Generally, you can expect to study at least 2 hours outside of class for every hour of class time. To get credit for homework you'll need to use an on-line homework site. We'll start with ILRN and then, after the first chapter on geometry, consider moving on to the WebAssign.
For ILRN, your account has already been created. Sign on as a returning user and then use your mycod email address
as your username and your 7-digit student number as your password.
QUIZZES: There will be regular quizzes throughout the semester. These measure your attendance and give you feedback on current topics of study.
GRADE: Your grade is a weighted average of homework, quiz, chapter test, & final exam scores:
a. Interpret slope as a constant rate of change.
b. Recognize and create linearity in tables, graphs, and/or equations.
c. Solve systems of equations by using methods of elimination, substitution and graphing.
d. Graph and/or find the equation of a circle given sufficient information.
e. Solve quadratic equations by factoring, completing the square, and the quadratic formula.
f. Recognize and create quadratic models for relations involving tables, graphs, and equations.
g. Graph a parabola by finding the vertex, intercepts, and other symmetric points.
h. Demonstrate understanding of definitions for function and its related terms: domain and range.
i. Use appropriate notation for function equations and for describing domain and range.
j. Demonstrate understanding of the exponential function, its scaling and growth factors.
k. Understand how to solve similar triangle problems.
l. Demonstrate understanding of triangle congruency theorems involving SSS, SAS, AAS.
m. Basic knowledge about congruence relations such as the congruence of vertical angles
n. Familiarity with Pythagorean theorem.
o. Demonstrate understanding of deductive reasoning in the construction of a proof.
Vectors including analytic and geometric representations and applications.
Course Objectives: Upon completion of this course, students will be able to:
Apply facts about angles, parallel lines and triangles to deduce further results about a geometric
figure.
Prove when two triangles are congruent or similar.
Justify the lengths of sides in an isosceles right triangle and in a 30-60-90 triangle.
Deduce the lengths of sides in quadrilaterals such as trapezoids and rectangles using basic definitions,
Pythagorean Theorem, perimeter and/or area.
Calculate the measure of a central angle in a circle using the measure of the intercepted arc and calculate the areas of geometric figures involving circles.
Apply facts about plane geometric figures to deduce the surface area and volume of three dimensional geometric figures.
Demonstrate an understanding of the concept of a function by identifying and describing a function graphically, numerically and algebraically.
Calculate the domain and range for a function expressed as a graph or an equation. From a graph, estimate the intervals where a function is increasing, decreasing and/or has a maximum or minimum value.
Use and interpret function notation to find "inputs" and "outputs" from the graph, table and/or an equation describing a function.
From an equation, graph or table, calculate average rates of change by using a difference quotient or by using slopes of secant lines. Analyze average rates of change to determine the concavity of a graph.
Demonstrate an understanding of the six basic transformations of functions by graphing translated functions including the quadratic functions.
Represent a word problem (especially a geometric problem) with a function.
Determine when a function has an inverse (one to one functions) and find the inverse function graphically or algebraically.
Form new functions through addition, subtraction, multiplication, division and composition.
Recognize classical and analytic definitions of the trigonometric functions.
Solve triangles using right triangle trigonometry, the law of sines and the law of cosines.
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Trigonometry - 10th edition
Summary
10th Edition. Used - Acceptable. Text is generally clean; has used stickers on cover. Does not include online code or other supplements unless noted. Choose EXPEDITED shipping for faster delivery!
$114.42
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Another problem that can be
clearly illustrated by using GSP is to find the shortest time taken to cross
the river. Suppose a current flows at a certain velocity w downstream. A boat
is steered at a constant speed v. The direction the course taken is to be
determined by the boat. The question is: what is the direction the boat should
steer in order to reach the other side of the bank in the shortest possible
time?
Figure 3
We construct the worksheet as in Figure 4 below.
In Figures 4 and 5 below, the unit of measurement of time is in second.
The students are asked to drag the arrow, the direction
of which represents the direction the boat is steered. Once decided on the
direction the boat be steered, the button ANIMATE POINT on the screen
can be clicked to demonstrate the path the actual boat travels (see Figure
5). The direction the boat travels represented by GE in Figure 5 will not
be the same as the direction of steer of the boat, represented by GD. The
point E represents the actual position of the boat while D is the position
of the boat if there is no current downstream. Both points D and E have the
same projection along the direction perpendicular to the two parallel river
banks.
Students click and drag the course taken by the boat to
allow for different choices of directions steered by the boat. By altering
the course to be taken by the boat, the actual path traveled by the boat will
be altered accordingly. This is immediately visible from the worksheet itself.
The students can then be asked to explore on the course taken by the boat
in order to reach the other shore in the quickest possible time by taking
different courses in still water.
Figure 4
Figure 5
The students will discover that the course that the boat
should take in order to reach the other shore in the quickest possible time
is that perpendicular to the two parallel banks. The mathematical rigors of
projection will be dispensed with while the objective is met.
As a bonus to the use of GSP
in this case, the students will be able to make the following observations
with the above file:
a. If the boatman steers upstream, the speed of the boat
is slowed down compared with the speed he steers, and hence it takes a longer
time to reach the other shore;
b. If the boatman steers downstream, the speed of the
boat is increased from the speed he steers the boat (the further downstream,
the faster the speed of the boat). However, the distance it has to take
to cross the river is much longer, hence the time taken to reach the other
shore is also increased.
Observations (a) and (b) above are difficult
to demonstrate with the mechanical computation itself; with the use of such
animation, the observations are quite visible to the students.
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At Teaching Tape, the videos are designed to meet the need of the homeschool teacher, student and others as a resource that establishes a solid foundation in math. These DVD's must be used with the Saxon Text or an incomplete understanding of concepts will be the result. They are meant to complement the textbook. There are 16 DVD's included in this program which are approximately 2 hours long. The cost of the set with text, tests, and answer kits would cost $335, but if one already has the text and tests, the DVD's alone are $265 and can be purchased all at once, in sets of 8, or individually. The greatest benefit of the program is that whoever is buying it has ownership and can pass it along to other families in desired.
I don't have a full understanding of Algebra but using these DVD's has given me a better idea of how easily that can be accomplished. The teacher is excellent, and I like the way she gives visual demonstrations as she clearly explains the concepts step by step. The teacher gives many helpful tips and that cuts the time to work a problem almost in half. I have used products from other publishers and none were more clearly demonstrated as this one is. I really felt comfortable listening to the teacher and her voice gave me more confidence in what I was doing in the concepts. These DVD's could bring great relief to many parents who do not display expertise in Math concepts. Once my daughter gets to this level of Algebra, we will be buying a textbook and using the DVD's for her studies.
Product Review by Nancy King, The Old Schoolhouse® Magazine, LLC, November 2008
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...Matrices are introduced, along with the basic trigonometric functions and their uses. Quadratics, conic sections, exponentials and logarithms will be new topics for students in Algebra II. In Geometry we deal with the shape, size and relative position of shapes
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Brings together ideas from PDE theory, General Relativity and Astrophysics
Valuable resource for advanced undergraduates, graduates and researchers in fields such as numerical relativity and cosmology which are currently very active
A graduate level text on a subject which brings together several areas of mathematics and physics: partial differential equations, differential geometry and general relativity. It explains the basics of the theory of partial differential equations in a form accessible to physicists and the basics of general relativity in a form accessible to mathematicians. In recent years the theory of partial differential equations has come to play an ever more important role in research on general relativity. This is partly due to the growth of the field of numerical
relativity, stimulated in turn by work on gravitational wave detection, but also due to an increased interest in general relativity among pure mathematicians working in the areas of partial differential equations and Riemannian geometry, who have realized the exceptional richness of the interactions between geometry and analysis which arise. This book provides the background for those wishing to learn about these topics. It treats key themes in general relativity including matter models and symmetry classes and gives an introduction to relevant aspects of the most important classes of partial differential equations, including ordinary differential equations, and material on functional analysis. These elements are brought together to discuss a variety of important examples in the field of
mathematical relativity, including asymptotically flat spacetimes, which are used to describe isolated systems, and spatially compact spacetimes, which are of importance in cosmology
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Number Theory and Geometry
This module runs in alternate years: 2012-13, 2014-15 and so on.
EMMS093S6 (30 credits)
Aims
This is a two-part course aiming to provide you with an introduction to two important areas of pure mathematics, number theory and geometry -- topics which every pure mathematician will find of interest.
The number theory section will cover types of numbers such as polygonal numbers and perfect numbers, followed by number theoretic functions, including Euler's φ function. We will prove Fermat's little theorem and study quadratic congruences as well as Pythagorean triples and sums of squares.
The section on geometry will devote time to vector geometry, affine geometry and Euclidean geometry. Curves arising from conic sections, such as the ellipse and the hyperbola, will also be studied and their properties derived from first principles, with some applications and generalisations. Finally there will be a look at the geometry of the complex plane assignment. The examination in the Summer Term has three sections. Section A (worth 40%) consists of compulsory short questions. Sections B and C (worth 20% each) contain several longer questions. You must answer one from Section B and one from Section C.
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Product Description
A beautifully-sequenced review of transformational geometry with the MIRA™, starting at a 7th grade level and moving upward. Includes plenty of activities for junior high students. Topics include properties of perpendicular lines, reflection, symmetry, and motion. 87 pages. Grade 7 and up.
Prices listed are U.S. Domestic prices only and apply to orders shipped within the United States. Orders from outside the
United States may be charged additional distributor, customs, and shipping charges.
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LearnKey Becoming Successful - Problem Solvers Set 1 this course, students will learn to analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns. At the conclusion of this course, students will be able to indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy and be able to apply them in other circumstances. Classroom activities and worksheets will involve students in learning about the problem-solving process.
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Math, ISSE, Reading, English Tutor"
...Real world applications are presented within the course content and a function's approach is emphasized. Prealgebra instruction includes a review of the basics of mathematics and a thorough introduction to integers, basic equations and word problems. This course is designed to develop the skills and understanding to perform the fundamental operations...
read more
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CAREER DEVELOPMENT
ASVAB/AFCT TESTS
THE
MATHEMATICS KNOWLEDGE (MK) TEST
The Mathematics Knowledge tests your
ability to use basic mathematical relationships such as algebra,
geometry, and trigonometry and your knowledge of math principles,
concepts, and procedures. It's essentially a continuation of the AR
(Arithmetic Reasoning) test.
25 questions in 24 minutes
Here are the types of subjects tested:
adding fractions with the same denominator
adding fractions with different
denominators
adding mixed numbers
subtracting fractions with different
denominators
subtracting mixed numbers with the same
denominator
subtracting mixed numbers with different
denominators
factoring
multiplying fractions
multiplying mixed numbers
multiplying percents
multiplication properties
dividing fractions
dividing percents
dividing mixed numbers
division properties
subtracting percents
adding percents
bases
subtracting fractions with the same
denominator
exponents
powers
reciprocals
factorial
prime numbers
roots
algebraic equations
geometry (types of angles, triangles,
circles, perimeter, area)
Commercially-available study guides and
first-year college math text books are the best way to study for this test.
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This textbook is written for everyone who has experienced challenges learning Calculus. This book really teaches you, helps you understand and master Calculus through clear and meaningful explanations…
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Mathematics is crucial to all aspects of engineering and technology. Understanding key mathematical concepts and applying them successfully to solve problems are vital skills every engineering student must acquire. This text teaches, applies and nurtures those skills. Mathematics for Engineers is informal, accessible and practically oriented. The material is structured so students build up their knowledge and understanding gradually. The interactive examples have been carefully designed to encourage students to engage fully in the problem-solving process. MyMathLab(r) is a series of text-specific, easily customizable online courses for Prentice Hall textbooks in mathematics and statistics. Powered by CourseCompass (Pearson Education's online teaching and learning environment) and MathXL(r) (our online homework, tutorial, and assessment system), MyMathLab gives you the tools you need to deliver all or a portion of your course online, whether your students are in a lab setting or working from home.
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Level I Honors Mathematics Courses cover the same material as College Prep but the pace of the course is accelerated and topics are covered in more detail and with greater emphasis on quantitative analysis.
Level II Honors Mathematics courses focus on developing and honing laboratory skills, critical thinking, problem solving, and independent analysis. Courses are rigorous and provide students with a solid foundation in preparation for further studies in science, mathematics, or engineering.
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good tutorial that many operations such as aplicad revolution, surfaces, sweep court and if I equeivoco rounding lso good tutorials apply a analizis of what is done in every part so the reader or learner understands in a way eficas
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Pittsview AlgebraTherefore math course that covers basic materials such as inequalities, absolute value, and so forth.
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Course
Accelerated GPS Pre-Calculus
Major Topics Covered
This is the third in a sequence of mathematics courses designed primarily to prepare students to take AB or BC Advanced Placement Calculus course. It includes general trigonometry and its functions; exponential, logarithmic, and higher degree polynomial functions as well as rational functions; parametric and polar curves and functions; sequences and series and applications from statistics. Instruction and assessment will include the appropriate use of manipulative and technology. Topics will be represented in multiple ways, such as concrete/pictorial, verbal/written, numeric/data-based, graphical, and symbolic methods. Concepts will be introduced and used, where appropriate, in the context of real life applications, projects and experiments.
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Algebra 2: Practice Workbook
Average rating
2 out of 5
Based on 2 Ratings and 2 Reviews
Book Description
Math concepts become ever-more challenging in the high school years. Some teenagers need support to insure understanding and to gain confidence in applying these concepts. Your child can get that support using Pearson products at home.
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Overview - PRE-ALGEBRA 2 - DATA ANALYSIS & STATS STUDENT TEXT 3
The pacing is slower, but the scope and sequence of the course remains the same as a regular pre-algebra course.
Pre-Algebra Curriculum is divided into two semesters to teach a full year's curriculum of pre-algebra. Written for middle school and high school students with learning differences, the content's reading level has been kept at 3.0–5.0 without sacrificing solid mathematics content.
Mathematics vocabulary essential to problem solving is defined and set in bold type in the student text. The complete curriculum includes three student texts per semester (for a total of six) and one teacher binder per semester.
STUDENT TEXTS Student texts include both easy-to-read lessons and pages for reinforcement. Each lesson is typically contained within two pages, and two worksheets follow the lesson. Extra practice sheets are included at the end of each student text. Students have the opportunity to learn, practice, and then review essential skills using multiple worksheets. Problems can be worked directly in the student text, which eliminates the need to transfer information. Word problems that focus on "real-world" skills are provided on most sheets.
TEACHER BINDER Each teacher binder complements the student texts, with identical lessons and at least one worksheet per lesson. Tips and guides are included to help the teacher instruct in the most efficient and understandable way. Each unit provides quizzes and tests to help assess mastery of skills. The answer key for each lesson, quiz, test, and student text practice sheet is provided at the end of each unit.
STANDARDSPre-Algebra Curriculum has been carefully written to comply with
the national standards and objectives. These standards help prepare students for standardized tests. The program can be used in self-contained and inclusive settings.
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Fifth Ed. - Word Problems
Description
The Word Problems Guide demystifies the most challenging of math questions on the GMAT—the word problem. This book equips students with broad, powerful strategies, as well as specific tools, for tackling GMAT word problems in all their various guises.
ISBN: 978-1-935707-68-4
$26.00
Online Resources
Your online resources will be activated immediately after your purchase and available for one year from that date. You can access these resources through the Manhattan GMAT Student Center after you receive your confirmation email.
6 Computer Adaptive Practice Exams
Manhattan GMAT's Computer Adaptive Exams adapt to your ability level and draw from a bank of more than 1200 unique questions of varying difficulty written by Manhattan GMAT's expert Instructors. Questions reflect the most up-to-date GMAT content, including the new Integrated Reasoning section.
Word Problems Online Question Bank
All questions included in this bank (25 total) draw from the subject of Word Problems and are written by Manhattan GMAT's expert Instructors. All Manhattan GMAT question banks include questions of varying difficulty levels.
Chapter by Chapter
Algebraic Translations
Pay Attention to Units; Common Relationships; Integer Constraints
Rates & Work
Basic Motion: The RTD Chart; Matching Units in the RTD Chart; Multiple Rates; Relative Rates; Average Rate: Don't Just Add and Divide; Basic Work Problems; Working Together: Add the Rates; Population Problems
Statistics
Averages; Using the Average Formula; Weighted Averages; Median: The Middle Number; Standard Deviation
Consecutive Integers
Evenly Spaced Sets; Properties of Evenly Spaced Sets; Counting Integers: Add One Before You Are Done; The Sum of Consecutive Integers
Overlapping Sets
Word Problem Strategies
Data Sufficiency Basics; What Does "Sufficient" Mean?; The DS Process; Putting It All Together; Putting It All Together (Again); Weighted Averages on Data Sufficiency; Replacing Variables with Numbers; Backsolving; Using Charts to Organize Variables
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books.google.fr - Introducing the reader to classical integrable systems and their applications, this book synthesizes the different approaches to the subject, providing a set of interconnected methods for solving problems in mathematical physics. The authors introduce and explain each method, and demonstrate how it can... to Classical Integrable Systems
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More About
This Textbook
Overview
Complex variables offer very efficient methods for attacking many difficult problems, and it is the aim of this book to offer a thorough review of these methods and their applications. Part I is an introduction to the subject, including residue calculus and transform methods. Part II advances to conformal mappings, and the study of Riemann-Hilbert problems. An extensive array of examples and exercises are included. This new edition has been improved throughout and is ideal for use in introductory undergraduate and graduate level courses in complex variables. First Edition Hb (1997): 0-521-48058-2 First Edition Pb (1997): 0-521-48523-1
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This course is aimed at seniors who want to continue to strengthen their understanding of mathematical concepts that they will need for success in careers, colleg math courses and decision-making in everyday life. The course will focus on personal and business finance, with students applying algebraic concepts to real-world topics. Algebraic concepts include ratios and percents, linear, quadratic, and exponential functions and work with data and statistics. A TI-83/84 graphing calculator is required.
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